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%I #12 Feb 06 2017 08:31:41
%S 0,0,0,1,0,1,0,3,1,3,1,8,3,9,6,16,9,24,17,35,29,49,45,81,73,110,115,
%T 166,166,240,250,347,372,491,539,715,776,988,1109,1393,1553,1935,2178,
%U 2676,3034,3674,4176,5056,5734,6862,7834,9316,10615,12576,14341,16890
%N Number of partitions of n such that the number of parts and the largest part and the smallest part are pairwise not coprime.
%C See comments in A199891, which apply to this sequence also.
%H Alois P. Heinz, <a href="/A200476/b200476.txt">Table of n, a(n) for n = 1..300</a>
%e a(8) = 3: [2,6], [4,4], [2,2,2,2];
%e a(9) = 1: [3,3,3];
%e a(10) = 3: [2,8], [4,6], [2,2,2,4];
%e a(11) = 1: [2,2,3,4];
%e a(12) = 8: [2,10], [4,8], [6,6], [3,3,6], [2,2,2,6], [2,2,4,4], [2,3,3,4], [2,2,2,2,2,2].
%p b:= proc(n, j, t, k) option remember;
%p add(b(n-i, i, t+1, k), i=j..iquo(n, 2))+
%p `if`(igcd(n, t)>1 and igcd(k, t)>1 and igcd(n, k)>1, 1, 0)
%p end:
%p a:= n-> add(b(n-j, j, 2, j), j=2..iquo(n, 2)):
%p seq(a(n), n=1..70);
%t b[n_, j_, t_, k_] := b[n, j, t, k] = Sum[b[n-i, i, t+1, k], {i, j, Quotient[n, 2]}] + If[GCD[n, t]>1 && GCD[k, t]>1 && GCD[n, k]>1, 1, 0]; a[n_] := Sum [b[n-j, j, 2, j], {j, 2, Quotient[n, 2]}]; Table[a[n], {n, 1, 70}] (* _Jean-François Alcover_, Feb 06 2017, translated from Maple *)
%Y Cf. A199891.
%K nonn
%O 1,8
%A _Alois P. Heinz_, Nov 18 2011
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