A340961 Number of ways to write n as an ordered sum of 5 primes.

1, 5, 10, 15, 25, 36, 50, 65, 70, 90, 110, 125, 155, 170, 200, 241, 270, 300, 350, 375, 435, 500, 530, 600, 640, 696, 760, 850, 840, 985, 990, 1170, 1160, 1370, 1250, 1570, 1445, 1760, 1600, 2000, 1710, 2340, 1950, 2555, 2165, 2876, 2320, 3340, 2560, 3595, 2880, 3985, 3050

Offset

10,2

Links

Seiichi Manyama, Table of n, a(n) for n = 10..10000

Formula

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

Maple

b:= proc(n, k) option remember; local r, p; r, p:= 0, 2;
      if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else
      while p<=n do r:= r+b(n-p, k-1); p:= nextprime(p) od; r fi
    end:
a:= n-> b(n, 5):
seq(a(n), n=10..62);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 62; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 10] &

Crossrefs

Column k=5 of A121303.

Cf. A000040, A010051, A073610, A098238, A259195, A340960, A340962, A340963, A340964, A340965, A340966.

Sequence in context: A151761 A008439 A276514 * A031471 A045206 A138521

Adjacent sequences: A340958 A340959 A340960 * A340962 A340963 A340964

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved