A284828 Expansion of Sum_{i>=2} x^prime(i)/(1 - x^prime(i)) * Product_{j>=i} 1/(1 - x^prime(j)).

0, 0, 1, 0, 1, 2, 1, 1, 3, 3, 3, 5, 4, 6, 9, 7, 10, 11, 12, 17, 19, 22, 23, 26, 33, 36, 41, 48, 52, 59, 66, 78, 85, 97, 112, 117, 134, 151, 169, 187, 207, 230, 255, 284, 313, 348, 379, 418, 465, 508, 561, 620, 674, 737, 812, 892, 972, 1064, 1157, 1257, 1379, 1503, 1639, 1776, 1935, 2101, 2279, 2483

Offset

1,6

Comments

Total number of smallest parts in all partitions of n into odd prime parts (A065091).

Links

Table of n, a(n) for n=1..68.

Index entries for related partition-counting sequences

Formula

G.f.: Sum_{i>=2} x^prime(i)/(1 - x^prime(i)) * Product_{j>=i} 1/(1 - x^prime(j)).

Example

a(16) = 7 because we have [13, 3], [11, 5], [7, 3, 3, 3], [5, 5, 3, 3] and 1 + 1 + 3 + 2 = 7.

Mathematica

nmax = 68; Rest[CoefficientList[Series[Sum[x^Prime[i]/(1 - x^Prime[i]) Product[1/(1 - x^Prime[j]), {j, i, nmax}], {i, 2, nmax}], {x, 0, nmax}], x]]

Prog

(PARI) x = 'x + O('x ^ 70); concat([0, 0], Vec(sum(i=2, 70, x^prime(i)/(1 - x^prime(i)) * prod(j=i, 70, 1/(1 - x^prime(j)))))) \\ Indranil Ghosh, Apr 05 2017

Crossrefs

Cf. A065091, A084993, A092268, A092269, A099773, A195820, A281544, A284827.

Sequence in context: A334347 A283672 A053268 * A101417 A318660 A301502

Adjacent sequences: A284825 A284826 A284827 * A284829 A284830 A284831

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2017

Status

approved