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

%I #15 Sep 21 2024 08:41:57

%S 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,

%T 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,

%U 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

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

%H Amiram Eldar, <a href="/A069935/b069935.txt">Table of n, a(n) for n = 0..10000</a>

%F From _Amiram Eldar_, May 25 2024: (Start)

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

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

%t a[n_] := 2^IntegerExponent[PartitionsP[n], 2]; Array[a, 100, 0] (* _Amiram Eldar_, May 25 2024 *)

%o (PARI) for(n=0,10^3,my(p=numbpart(n));print1(2^valuation(p,2),", ")); \\ _Joerg Arndt_, May 09 2013

%Y Cf. A000041, A006519, A278478.

%K nonn

%O 0,3

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

%E More terms from _John W. Layman_, May 09 2002