A069935 Maximal power of 2 that divides the n-th partition number.

1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 8, 1, 1, 1, 16, 1, 1, 1, 2, 1, 8, 2, 1, 1, 2, 4, 2, 2, 1, 4, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 4, 1, 2, 4, 4, 1, 1, 4, 1, 2, 2, 64, 1, 1, 1, 32, 1, 1, 1, 4, 8, 1, 1, 4, 2, 4, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 8, 1, 2048, 2, 8, 1, 4, 2, 1, 2, 1, 1, 16, 1

Offset: 0

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 04 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000041, A006519, A278478.

Programs

Mathematica

a[n_] := 2^IntegerExponent[PartitionsP[n], 2]; Array[a, 100, 0] (* Amiram Eldar, May 25 2024 *)

PARI

for(n=0,10^3,my(p=numbpart(n));print1(2^valuation(p,2),", ")); \\ Joerg Arndt, May 09 2013

Formula

From Amiram Eldar, May 25 2024: (Start)

a(n) = A006519(A000041(n)).

a(n) = 2^A278478(n). (End)

Extensions

More terms from John W. Layman, May 09 2002