%I #13 Sep 08 2022 08:46:08
%S 5,10,11,12,16,18,19,24,26,27,33,37,39,40,41,47,48,52,53,54,55,61,68,
%T 75,76,82,83,89,96,97,103,110,111,117,124,125,131,138,140,145,147,152,
%U 159,166,170,173,177,180,187,191,194,201,208,213,215,222,225,229,232
%N Numbers m such that 7 divides A000041(m).
%H Bruno Berselli, <a href="/A243936/b243936.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Range[250], Mod[PartitionsP[#], 7] == 0 &]
%o (Sage)
%o # From _Peter Luschny_ in A000041
%o @CachedFunction
%o def A000041(n):
%o if n == 0: return 1
%o S = 0; J = n-1; k = 2
%o while 0 <= J:
%o T = A000041(J)
%o S = S+T if is_odd(k//2) else S-T
%o J -= k if is_odd(k) else k//2
%o k += 1
%o return S
%o [n for n in (0..250) if mod(A000041(n),7) == 0]
%o (Magma) [n: n in [1..250] | IsZero(NumberOfPartitions(n) mod 7)];
%o (PARI) is(n)=numbpart(n)%7==0 \\ _Charles R Greathouse IV_, Apr 08 2015
%Y Numbers m such that k divides A000041(m), where k is prime: A001560 (k=2), A083214 (k=3), A243935 (k=5), this sequence (k=7), A027827 (k=11), A071750 (k=13). For k composite: A237278 (k=4), A035700 (k=12).
%K nonn,easy
%O 1,1
%A _Bruno Berselli_, Jun 15 2014