A284827 Expansion of Sum_{i>=1} x^prime(i)/(1 - x^prime(i)) * Product_{j>=i} 1/(1 - x^prime(j)).

0, 1, 1, 2, 2, 5, 4, 6, 9, 11, 13, 18, 20, 26, 34, 37, 47, 55, 66, 80, 96, 111, 130, 150, 180, 206, 240, 278, 318, 366, 419, 483, 549, 626, 716, 803, 913, 1034, 1167, 1314, 1477, 1659, 1861, 2085, 2332, 2605, 2902, 3232, 3602, 3999, 4442, 4930, 5454, 6034, 6675, 7375, 8133, 8967, 9870, 10855

Offset

1,4

Comments

Total number of smallest parts in all partitions of n into prime parts.

Links

Table of n, a(n) for n=1..60.

Index entries for related partition-counting sequences

Formula

G.f.: Sum_{i>=1} x^prime(i)/(1 - x^prime(i)) * Product_{j>=i} 1/(1 - x^prime(j)).

Example

a(10) = 11 because we have [7, 3], [5, 5], [5, 3, 2], [3, 3, 2, 2], [2, 2, 2, 2, 2] and 1 + 2 + 1 + 2 + 5 = 11.

Mathematica

nmax = 60; Rest[CoefficientList[Series[Sum[x^Prime[i]/(1 - x^Prime[i]) Product[1/(1 - x^Prime[j]), {j, i, nmax}], {i, 1, nmax}], {x, 0, nmax}], x]]

Crossrefs

Cf. A000607, A084993, A092268, A092269, A195820, A284828.

Sequence in context: A098366 A284127 A261114 * A241306 A336073 A266792

Adjacent sequences: A284824 A284825 A284826 * A284828 A284829 A284830

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2017

Status

approved