A341985 Number of ways to write n as an ordered sum of 6 primes (counting 1 as a prime).

1, 6, 21, 50, 96, 156, 237, 336, 465, 596, 747, 882, 1077, 1260, 1536, 1736, 2067, 2286, 2761, 3030, 3627, 3842, 4578, 4806, 5826, 6000, 7167, 7116, 8562, 8430, 10318, 9906, 12093, 11396, 14286, 13386, 16868, 15270, 19242, 17180, 22218, 19536, 25393, 21750, 28680, 24456

Offset: 6

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

• nonn

Crossrefs

Cf. A008578, A280917, A283762, A340962, A341949, A341977, A341982, A341983, A341984, A341986, A341987, A341988, A341989.

Programs

Mathematica

nmax = 51; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^6.