A363252 - OEIS

%I #11 May 24 2023 03:55:08

%S 1,1,1,1,1,1,1,5,2,2,2,4,1,1,1,1,1,1,1,2,1,4,1,1,1,2,3,2,2,1,4,2,3,7,

%T 2,3,1,1,1,1,21,21,2,1,1,2,6,14,3,1,2,1,1,1,1,2,1,3,4,4,17,1,2,1,2,2,

%U 4,1,3,5,1,1,1,1,2,2,1,1,2,2,4,1,1,1,2,11,2

%N a(n) = gcd(A000041(n), A000009(n)).

%p b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(

%p      `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)

%p     end:

%p a:= n-> igcd(b(n), combinat[numbpart](n)):

%p seq(a(n), n=0..120);  # _Alois P. Heinz_, May 23 2023

%t Table[GCD[PartitionsP[n], PartitionsQ[n]], {n, 0, 100}]

%Y Cf. A000009, A000041, A051177, A056848, A093952, A304991.

%K nonn

%O 0,8

%A _Vaclav Kotesovec_, May 23 2023, inspired by _Zhi-Wei Sun_