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A114912 2^a(n) divides A000009(n) but 2^(a(n)+1) does not. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..101.

K. 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.

FORMULA

a(n) = A007814(A000009(n)) [From Max Alekseyev, Apr 27 2010]

CROSSREFS

The 0's are in A001318. The 1's are in A114913. Least inverse A115251.

Sequence in context: A044942 A263401 A239928 * A231723 A029274 A239498

Adjacent sequences:  A114909 A114910 A114911 * A114913 A114914 A114915

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 06 2006

STATUS

approved

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Last modified February 19 20:17 EST 2019. Contains 320328 sequences. (Running on oeis4.)