cp's OEIS Frontend

A200727 Number of partitions of n such that the number of parts is not divisible by the greatest part.

%I A200727 #15 Feb 06 2017 12:09:40
%S A200727 0,1,1,3,4,8,9,16,22,33,42,61,79,110,143,192,246,325,411,535,676,865,
%T A200727 1081,1371,1704,2136,2642,3283,4035,4979,6082,7453,9067,11043,13365,
%U A200727 16197,19516,23531,28239,33894,40513,48425,57667,68661,81497,96679,114370
%N A200727 Number of partitions of n such that the number of parts is not divisible by the greatest part.
%C A200727 Also number of partitions of n such that the greatest part is not divisible by the number of parts.  Equivalence can be shown using Ferrers-Young diagrams.
%H A200727 Alois P. Heinz, <a href="/A200727/b200727.txt">Table of n, a(n) for n = 1..500</a>
%e A200727 The number of parts is not divisible by the greatest part:
%e A200727 a(5) = 4: [1,2,2], [2,3], [1,4], [5];
%e A200727 a(6) = 8: [1,1,1,1,2], [2,2,2], [1,1,1,3], [3,3], [1,1,4], [2,4], [1,5], [6].
%e A200727 The greatest part is not divisible by the number of parts:
%e A200727 a(5) = 4: [1,1,1,1,1], [1,1,1,2], [1,2,2], [2,3];
%e A200727 a(6) = 8: [1,1,1,1,1,1], [1,1,1,1,2], [1,1,2,2], [2,2,2], [1,1,1,3], [3,3], [1,1,4], [1,5].
%p A200727 b:= proc(n, j, t) option remember;
%p A200727       add(b(n-i, i, t+1), i=j..iquo(n, 2))+
%p A200727       `if`(irem(t, n)>0, 1, 0)
%p A200727     end:
%p A200727 a:= n-> b(n, 1, 1):
%p A200727 seq(a(n), n=1..50);
%t A200727 b[n_, j_, t_] := b[n, j, t] = Sum[b[n-i, i, t+1], {i, j, Quotient[n, 2]}] + If[Mod[t, n]>0, 1, 0]; a[n_] := b[n, 1, 1]; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Feb 05 2017, translated from Maple *)
%Y A200727 Cf. A199884, A199885.
%K A200727 nonn
%O A200727 1,4
%A A200727 _Alois P. Heinz_, Nov 21 2011