A364525 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.

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

Offset

1,5

Links

Table of n, a(n) for n=1..36.

Mathematica

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}]

Crossrefs

Cf. A000720.

Cf. A166444.

Cf. A365062 (sum of pi(x) + 1 for n>0).

Sequence in context: A321408 A289976 A068036 * A077947 A077972 A293354

Adjacent sequences: A364522 A364523 A364524 * A364526 A364527 A364528

Keyword

nonn

Author

Robert P. P. McKone, Dec 22 2023

Status

approved