Commit 2026-10-19 02:37 388bcfe6

doc: add oeis attributes (#44370) This PR adds a batch of 61 @[oeis] attributes.

#	OEIS link	Mathlib doc link	description	OEIS terms	note
1	A000290	IsSquare	squares	0, 1, 4, 9, 16, 25, 36, 49, …	general monoid predicate; take α = ℕ
2	A005843	Even	nonnegative even numbers	0, 2, 4, 6, 8, 10, 12, 14, …	to_additive sibling of IsSquare; take α = ℕ
3	A005408	Odd	odd numbers	1, 3, 5, 7, 9, 11, 13, 15, …	general semiring predicate; take α = ℕ
4	A005117	Squarefree	squarefree numbers	1, 2, 3, 5, 6, 7, 10, 11, …	general monoid predicate; take R = ℕ
5	A000796	Real.pi	decimal digits of pi	3, 1, 4, 1, 5, 9, 2, 6, …	decimal expansion
6	A000166	numDerangements	derangements (subfactorials)	1, 0, 1, 2, 9, 44, 265, 1854, …
7	A000110	Nat.bell	Bell numbers	1, 1, 2, 5, 15, 52, 203, 877, …
8	A000108	catalan	Catalan numbers	1, 1, 2, 5, 14, 42, 132, 429, …
9	A000009	Nat.Partition.odds	partitions into odd parts	1, 1, 1, 2, 2, 3, 4, 5, …
10	A000009	Nat.Partition.distincts	partitions into distinct parts	1, 1, 1, 2, 2, 3, 4, 5, …
11	A001318	pentagonal	generalized pentagonal numbers	0, 1, 2, 5, 7, 12, 15, 22, …	to match oeis, one can use this #MWE
12	A000326	pentagonal	pentagonal numbers	0, 1, 5, 12, 22, 35, 51, 70, …	matched with oeis when k ≥ 0
13	A006318	Nat.largeSchroder	large Schroeder numbers	1, 2, 6, 22, 90, 394, 1806, 8558, …
14	A001003	Nat.smallSchroder	little Schroeder numbers	1, 1, 3, 11, 45, 197, 903, 4279, …
15	A132393	Nat.stirlingFirst	unsigned Stirling numbers, first kind	1, 0, 1, 0, 1, 1, 0, 2, …	triangle, read by rows
16	A048993	Nat.stirlingSecond	Stirling numbers, second kind	1, 0, 1, 0, 1, 1, 0, 1, …	triangle, read by rows
17	A000045	Int.fib	Fibonacci numbers	0, 1, 1, 2, 3, 5, 8, 13, …	ℤ-valued version
18	A007318	Nat.choose	Pascal's triangle	1, 1, 1, 1, 2, 1, 1, 3, …	triangle, read by rows
19	A059481	Nat.multichoose	multiset coefficients	1, 1, 1, 1, 2, 3, 1, 3, …	triangle, read by rows
20	A000984	Nat.centralBinom	central binomial coefficients	1, 2, 6, 20, 70, 252, 924, 3432, …
21	A000142	Nat.factorial	factorials	1, 1, 2, 6, 24, 120, 720, 5040, …
22	A006882	Nat.doubleFactorial	double factorials	1, 1, 2, 3, 8, 15, 48, 105, …
23	A000178	Nat.superFactorial	superfactorials	1, 1, 2, 12, 288, 34560, 24883200, 125411328000, …
24	A027746	Nat.primeFactorsList	prime factors with multiplicity	1, 2, 3, 2, 2, 5, 2, 3, …	irregular triangle, read by rows
25	A000045	Nat.fib	Fibonacci numbers	0, 1, 1, 2, 3, 5, 8, 13, …
26	A006530	Nat.maxPrimeFac	greatest prime factor	1, 2, 3, 2, 5, 3, 7, 2, …	a(1) = 1 convention
27	A000040	Nat.Prime	the primes	2, 3, 5, 7, 11, 13, 17, 19, …
28	A020639	Nat.minFac	least prime factor	1, 2, 3, 2, 5, 2, 7, 2, …	a(1) = 1 convention
29	A027748	Nat.primeFactors	distinct prime factors	1, 2, 3, 2, 5, 2, 3, 7, …	irregular triangle, read by rows
30	A000010	Nat.totient	Euler totient	1, 1, 2, 2, 4, 2, 6, 4, …
31	A001358	Nat.IsSemiprime	semiprimes	4, 6, 9, 10, 14, 15, 21, 22, …	predicate
32	A002322	ArithmeticFunction.carmichael	Carmichael lambda	1, 1, 2, 2, 4, 2, 6, 2, …
33	A008836	ArithmeticFunction.liouville	Liouville lambda	1, -1, -1, 1, -1, 1, -1, -1, …	matched with oeis when z ≥ 1
34	A001477	ArithmeticFunction.id	the nonnegative integers	0, 1, 2, 3, 4, 5, 6, 7, …
35	A001222	ArithmeticFunction.cardFactors	Omega(n): prime factors with multiplicity	0, 1, 1, 2, 1, 2, 1, 3, …
36	A001221	ArithmeticFunction.cardDistinctFactors	omega(n): distinct prime factors	0, 1, 1, 1, 1, 2, 1, 1, …
37	A008683	ArithmeticFunction.moebius	Moebius mu	1, -1, -1, 0, -1, 1, -1, 0, …	matched with oeis when z ≥ 1
38	A057427	ArithmeticFunction.zeta	1 for n >= 1, 0 at n = 0	0, 1, 1, 1, 1, 1, 1, 1, …
39	A164555	bernoulli'	numerators of the "original" Bernoulli numbers	1, 1, 1, 0, -1, 0, 1, 0, …	numerator
40	A027642	bernoulli'	denominators of Bernoulli numbers	1, 2, 6, 1, 30, 1, 42, 1, …	denominator
41	A027641	bernoulli	numerators of Bernoulli numbers	1, -1, 1, 0, -1, 0, 1, 0, …	numerator
42	A027642	bernoulli	denominators of Bernoulli numbers	1, 2, 6, 1, 30, 1, 42, 1, …	denominator
43	A002997	Nat.IsCarmichael	Carmichael numbers	561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, …	predicate
44	A003418	Nat.lcmUpto	lcm of {1, ..., n}	1, 1, 2, 6, 12, 60, 60, 420, …
45	A027750	Nat.divisors	divisors	1, 1, 2, 1, 3, 1, 2, 4, …	triangle, read by rows
46	A027751	Nat.properDivisors	proper divisors	1, 1, 1, 1, 2, 1, 1, 2, …	irregular triangle, read by rows
47	A000396	Nat.Perfect	perfect numbers	6, 28, 496, 8128, 33550336, …
48	A005101	Nat.Abundant	abundant numbers	12, 18, 20, 24, 30, 36, 40, 42, …
49	A005100	Nat.Deficient	deficient numbers	1, 2, 3, 4, 5, 7, 8, 9, …
50	A005835	Nat.Pseudoperfect	pseudoperfect numbers	6, 12, 18, 20, 24, 28, 30, 36, …
51	A006037	Nat.Weird	weird numbers	70, 836, 4030, 5830, 7192, 7912, 9272, 10430, …
52	A000215	Nat.fermatNumber	Fermat numbers	3, 5, 17, 257, 65537, …
53	A001008	harmonic	numerators of H(n)	1, 3, 11, 25, 137, 49, 363, 761, …	numerator
54	A002805	harmonic	denominators of H(n)	1, 2, 6, 12, 60, 20, 140, 280, …	denominator
55	A001620	Real.eulerMascheroniConstant	decimal digits of the Euler-Mascheroni constant	5, 7, 7, 2, 1, 5, 6, 6, …	decimal expansion
56	A000225	mersenne	Mersenne numbers 2^n - 1	0, 1, 3, 7, 15, 31, 63, 127, …
57	A003010	LucasLehmer.s	Lucas-Lehmer sequence	4, 14, 194, 37634, 1416317954, …
58	A230980	Nat.primeCounting	prime-counting pi(n)	0, 0, 1, 2, 2, 3, 3, 4, 4, …
59	A034386	primorial	primorials n#	1, 1, 2, 6, 6, 30, 30, 210, …
60	A001622	Real.goldenRatio	decimal digits of the golden ratio	1, 6, 1, 8, 0, 3, 3, 9, …	decimal expansion
61	A000005	ArithmeticFunction.sigma	sum of kth powers of divisors	1, 2, 2, 3, 2, 4, 2, 4, …	values for k = 0, n > 0