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Number of partitions of n such that the smallest part is divisible by the number of parts.

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`%I #15 Jan 20 2022 10:18:02
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`%S 1,1,1,2,2,2,2,3,4,4,5,6,7,7,8,10,11,13,15,18,20,23,25,29,33,36,41,47,
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`%T 53,58,66,74,83,92,103,116,130,144,160,179,199,219,243,269,298,328,
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`%U 362,399,441,484,533,586,645,708,778,854,937,1026,1124,1230,1347,1470,1607,1756,1917,2089
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`%N Number of partitions of n such that the smallest part is divisible by the number of parts.
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`%H Seiichi Manyama, <a href="/A168656/b168656.txt">Table of n, a(n) for n = 1..10000</a>
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`%F G.f.: Sum_{k>=1} x^(k^2)/((1-x^(k^2)) * Product_{i=1..k-1} (1-x^i)).
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`%o (PARI)
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`%o N=100; x='x+O('x^N);
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`%o Vec( sum(k=1,sqrtint(N), x^(k^2)/(1-x^(k^2)) / prod(i=1,k-1, 1-x^i) ) )
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`%Y Cf. A000041, A073336, A079501, A168655, A168657, A168659.
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`%K easy,nonn
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`%O 1,4
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`%A _Vladeta Jovovic_, Dec 01 2009, Dec 04 2009
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