A284834 Expansion of Sum_{i>=2} x^prime(i)/(1 - x^prime(i)) * Product_{j=2..i} 1/(1 - x^prime(j)).

0, 0, 1, 0, 1, 2, 1, 1, 3, 3, 2, 5, 4, 4, 9, 5, 6, 12, 8, 11, 17, 12, 14, 23, 19, 21, 29, 27, 29, 41, 37, 36, 56, 49, 55, 72, 62, 74, 91, 90, 96, 116, 117, 125, 155, 149, 162, 195, 194, 215, 246, 248, 270, 311, 324, 344, 389, 406, 435, 494, 509, 546, 615, 636, 694, 763, 787, 861, 942, 994, 1063

Offset

1,6

Comments

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

Links

Table of n, a(n) for n=1..71.

Index entries for related partition-counting sequences

Formula

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

Example

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

Mathematica

nmax = 64; Rest[CoefficientList[Series[Sum[x^Prime[i]/(1 - x^Prime[i]) Product[1/(1 - x^Prime[j]), {j, 2, i}], {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=2, i, 1/(1 - x^prime(j)))))) \\ Indranil Ghosh, Apr 04 2017

Crossrefs

Cf. A046746, A065091, A084993, A092311, A099773, A284828.

Sequence in context: A127838 A017817 A363567 * A279677 A262180 A308028

Adjacent sequences: A284831 A284832 A284833 * A284835 A284836 A284837

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2017

Status

approved