A341976 Number of partitions of n into 5 distinct primes (counting 1 as a prime).

1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 3, 1, 4, 0, 3, 2, 6, 2, 6, 2, 7, 5, 9, 4, 10, 5, 10, 8, 12, 7, 12, 8, 15, 12, 16, 12, 18, 14, 20, 17, 22, 18, 23, 20, 27, 26, 29, 27, 30, 30, 33, 36, 36, 36, 35, 41, 43, 48, 43, 49, 43, 56, 52, 61, 51, 64, 52, 73, 64, 77, 58, 82, 64, 93

Offset

18,7

Links

Table of n, a(n) for n=18..91.

Maple

b:= proc(n, i) option remember; series(`if`(n=0, 1,
     `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i-1)))(
     `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 6)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 5):
seq(a(n), n=18..91);  # Alois P. Heinz, Feb 24 2021

Mathematica

b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
     If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i - 1]]][
     If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 6}];
a[n_] := Coefficient[b[n, PrimePi[n]], x, 5];
Table[a[n], {n, 18, 100}] (* Jean-François Alcover, Jul 13 2021, after Alois P. Heinz *)

Crossrefs

Cf. A008578, A036497, A219199, A341948, A341973, A341974, A341975, A341977.

Sequence in context: A029185 A029184 A179049 * A029221 A304034 A029183

Adjacent sequences: A341973 A341974 A341975 * A341977 A341978 A341979

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved