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A243936 Numbers m such that 7 divides A000041(m).

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