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A364525
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a(n) is the number of distinct ways to partition the set {1,2,...,n} into nonempty subsets such that the sum of the pi(x)*(pi(x) + 1)/2 values of each subset's size x equals n, where pi() is the prime counting function given by A000720.
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0
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0, 0, 1, 1, 2, 5, 9, 18, 36, 73, 145, 290, 580, 1159, 2319, 4637, 9273, 18544, 37083, 74157, 148330, 296658, 593311, 1186613, 2373208, 4746380, 9492687, 18985447, 37970821, 75941497, 151882704, 303764828, 607528497, 1215054675, 2430104713, 4860217541
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OFFSET
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1,5
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LINKS
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MATHEMATICA
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p[n_] := p[n] = PrimePi[n];
pv[n_] := pv[n] = p[n]*(p[n] + 1)/2;
v[n_, k_] := v[n, k] = Module[{c = 0, i = 1}, If[k == 1, Return[If[pv[n] == n, 1, 0]]]; While[i < n - k + 2, If[pv[i] <= n, c += v[n - i, k - 1]]; i++]; c];
a[n_] := a[n] = Module[{c = 0, k = 1}, While[k <= n, c += v[n, k]; k++]; c]; Table[a[n], {n, 1, 36}]
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CROSSREFS
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Cf. A365062 (sum of pi(x) + 1 for n>0).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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