A341984 Number of ways to write n as an ordered sum of 5 primes (counting 1 as a prime).

1, 5, 15, 30, 50, 71, 100, 130, 170, 195, 231, 250, 310, 340, 420, 430, 525, 535, 685, 680, 851, 800, 1025, 970, 1280, 1145, 1470, 1250, 1685, 1440, 1991, 1600, 2230, 1790, 2615, 2070, 2985, 2190, 3250, 2410, 3700, 2665, 4125, 2840, 4560, 3200, 5135, 3470, 5670, 3705, 6226, 4120

Offset: 5

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

• nonn

Crossrefs

Cf. A008578, A280917, A283762, A340961, A341948, A341976, A341982, A341983.

Programs

Maple

b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
      `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 6)
    end:
a:= n-> coeff(b(n), x, 5):
seq(a(n), n=5..56);  # Alois P. Heinz, Feb 24 2021

Mathematica

nmax = 56; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^5.