OFFSET
0,7
COMMENTS
Almost all members of A000009 are divisible by 2^k for any k, therefore almost all a(n)>k for any k.
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..10000
Krishnaswami Alladi, Partition Identities Involving Gaps and Weights, Transactions of the American Mathematical Society, Vol. 349, No. 12 (Dec 1997), pp. 5001-5019.
Basil Gordon and Ken Ono, Divisibility of certain partition functions by powers of primes, The Ramanujan Journal, Vol. 1, No. 1 (1997), pp. 25-34; alternative link.
FORMULA
MATHEMATICA
a[n_] := IntegerExponent[PartitionsQ[n], 2]; Array[a, 100, 0] (* Amiram Eldar, Aug 24 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 06 2006
STATUS
approved