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%I #11 Feb 15 2017 06:20:20
%S 0,0,0,1,1,1,1,3,4,5,7,10,12,15,18,25,30,39,47,62,74,94,113,144,173,
%T 215,261,324,390,476,571,697,832,1004,1196,1439,1706,2038,2409,2868,
%U 3380,4001,4702,5550,6504,7645,8938,10478,12218,14277,16612,19363,22481
%N Number of partitions of n such that the number of parts and the smallest part are not coprime.
%H Alois P. Heinz, <a href="/A201025/b201025.txt">Table of n, a(n) for n = 1..400</a>
%F a(n) = A000041(n) - A200928(n).
%e a(7) = 1: [2,5];
%e a(8) = 3: [2,2,2,2], [4,4], [2,6];
%e a(9) = 4: [2,2,2,3], [3,3,3], [4,5], [2,7];
%e a(10) = 5: [2,2,3,3], [2,2,2,4], [3,3,4], [4,6], [2,8];
%e a(11) = 7: [2,3,3,3], [2,2,3,4], [3,4,4], [2,2,2,5], [3,3,5], [4,7], [2,9].
%p b:= proc(n, j, t, s) option remember;
%p add (b(n-i, i, irem(t+1, s), s), i=j..iquo(n, 2))+
%p `if`(igcd(t, s)>1, 1, 0)
%p end:
%p a:= n-> add (b(n-i, i, 2, i), i=2..iquo(n, 2)):
%p seq (a(n), n=1..60);
%t b[n_, j_, t_, s_] := b[n, j, t, s] = Sum[b[n-i, i, Mod[t+1, s], s], {i, j, Quotient[n, 2]}] + If[GCD[t, s]>1, 1, 0]; a[n_] := Sum [b[n-i, i, 2, i], {i, 2, Quotient[n, 2]}]; Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, Feb 15 2017, translated from Maple *)
%Y Cf. A000041, A199889, A200928.
%K nonn
%O 1,8
%A _Alois P. Heinz_, Nov 25 2011
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