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A114912
2^a(n) divides A000009(n) but 2^(a(n)+1) does not.
3
0, 0, 0, 1, 1, 0, 2, 0, 1, 3, 1, 2, 0, 1, 1, 0, 5, 1, 1, 1, 6, 2, 0, 3, 1, 1, 0, 6, 1, 8, 3, 2, 1, 6, 9, 0, 2, 3, 5, 1, 0, 2, 1, 1, 3, 11, 8, 1, 1, 6, 1, 0, 1, 10, 1, 1, 2, 0, 3, 6, 7, 2, 1, 9, 2, 3, 2, 1, 13, 1, 0, 5, 9, 1, 1, 1, 1, 0, 1, 3, 9, 2, 6, 1, 1, 6, 6, 1, 1, 1, 1, 11, 0, 5, 6, 1, 2, 8, 6, 1, 0, 1
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
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
a(n) = A007814(A000009(n)). - Max Alekseyev, Apr 27 2010
MATHEMATICA
a[n_] := IntegerExponent[PartitionsQ[n], 2]; Array[a, 100, 0] (* Amiram Eldar, Aug 24 2024 *)
CROSSREFS
Cf. A001318 (positions of 0's), A114913 (positions of 1's), A115251 (least inverse).
Sequence in context: A263401 A369814 A239928 * A231723 A342720 A029274
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 06 2006
STATUS
approved