A281853 Expansion of Sum_{k>=2} x^prime(k) / (1 - Sum_{k>=2} x^prime(k))^2.

0, 0, 1, 0, 1, 2, 1, 4, 3, 6, 10, 8, 19, 22, 26, 48, 53, 78, 112, 136, 205, 264, 354, 504, 639, 890, 1204, 1568, 2173, 2868, 3826, 5192, 6839, 9214, 12295, 16296, 21894, 28996, 38624, 51552, 68230, 90930, 120715, 159988, 212728, 281696, 373574, 495312, 655365, 868510, 1149161, 1520020, 2011591, 2658416, 3514446

Offset

1,6

Comments

Total number of parts in all compositions (ordered partitions) of n into odd primes (A065091).

Links

Table of n, a(n) for n=1..55.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=2} x^prime(k) / (1 - Sum_{k>=2} x^prime(k))^2.

Example

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

Mathematica

nmax = 55; Rest[CoefficientList[Series[Sum[x^Prime[k], {k, 2, nmax}]/(1 - Sum[x^Prime[k], {k, 2, nmax}])^2, {x, 0, nmax}], x]]

Crossrefs

Cf. A002124, A065091, A121304.

Sequence in context: A105361 A370728 A125154 * A077912 A077963 A114861

Adjacent sequences: A281850 A281851 A281852 * A281854 A281855 A281856

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2017

Status

approved