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A243935 Numbers m such that 5 divides A000041(m).

%I A243935 #17 Sep 08 2022 08:46:08
%S A243935 4,7,9,14,18,19,23,24,27,29,34,38,39,44,49,54,58,59,61,64,66,68,69,71,
%T A243935 74,79,82,84,89,94,97,99,103,104,109,114,119,120,124,127,128,129,130,
%U A243935 134,136,139,140,142,144,149,154,159,163,164,165,169,170,173,174
%N A243935 Numbers m such that 5 divides A000041(m).
%H A243935 Bruno Berselli, <a href="/A243935/b243935.txt">Table of n, a(n) for n = 1..1000</a>
%t A243935 Select[Range[200], Mod[PartitionsP[#], 5] == 0 &]
%o A243935 (Sage)
%o A243935 # From _Peter Luschny_ in A000041
%o A243935 @CachedFunction
%o A243935 def A000041(n):
%o A243935     if n == 0: return 1
%o A243935     S = 0; J = n-1; k = 2
%o A243935     while 0 <= J:
%o A243935         T = A000041(J)
%o A243935         S = S+T if is_odd(k//2) else S-T
%o A243935         J -= k if is_odd(k) else k//2
%o A243935         k += 1
%o A243935     return S
%o A243935 [n for n in (0..200) if mod(A000041(n),5) == 0]
%o A243935 (Magma) [n: n in [1..200] | IsZero(NumberOfPartitions(n) mod 5)];
%o A243935 (PARI) is(n)=numbpart(n)%5==0 \\ _Charles R Greathouse IV_, Apr 08 2015
%Y A243935 Numbers m such that k divides A000041(m), where k is prime: A001560 (k=2), A083214 (k=3), this sequence (k=5), A243936 (k=7), A027827 (k=11), A071750 (k=13). For k composite: A237278 (k=4), A035700 (k=12).
%K A243935 nonn,easy
%O A243935 1,1
%A A243935 _Bruno Berselli_, Jun 15 2014