A341977 Number of partitions of n into 6 distinct primes (counting 1 as a prime).

1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 1, 5, 0, 4, 1, 5, 2, 8, 1, 7, 2, 8, 4, 12, 2, 12, 6, 14, 7, 17, 5, 18, 8, 20, 11, 26, 10, 27, 15, 30, 18, 36, 17, 36, 22, 41, 28, 48, 25, 49, 35, 56, 40, 61, 38, 64, 50, 73, 56, 77, 54, 82, 70, 93, 74, 96, 78, 106, 92, 114, 100

Offset

29,7

Links

Alois P. Heinz, Table of n, a(n) for n = 29..10000

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, 7)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 6):
seq(a(n), n=29..100);  # Alois P. Heinz, Feb 24 2021

Mathematica

m = 6;
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, m + 1}];
a[n_] :=  Coefficient[b[n, PrimePi[n]], x, m];
Table[a[n], {n, 29, 100}] (* Jean-François Alcover, Mar 06 2021, after Alois P. Heinz *)

Crossrefs

Cf. A008578, A036497, A219200, A341949, A341973, A341974, A341975, A341976.

Sequence in context: A025815 A219199 A029225 * A309937 A116127 A039979

Adjacent sequences: A341974 A341975 A341976 * A341978 A341979 A341980

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved