A341981 Number of partitions of n into 10 distinct primes (counting 1 as a prime).

1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 5, 0, 4, 0, 2, 0, 9, 0, 7, 1, 7, 1, 14, 0, 10, 0, 12, 2, 22, 0, 19, 2, 22, 3, 34, 1, 31, 4, 32, 5, 54, 3, 48, 7, 50, 9, 78, 7, 70, 11, 76, 16, 113, 9, 100, 19, 114, 26, 155, 17, 147, 32, 164, 37, 212, 26

Offset

101,13

Links

Table of n, a(n) for n=101..174.

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, 11)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 10):
seq(a(n), n=101..174);  # 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, 11}];
a[n_] := Coefficient[b[n, PrimePi[n]], x, 10];
Table[a[n], {n, 101, 174}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A008578, A036497, A219204, A341972, A341973, A341974, A341975, A341976, A341977, A341978, A341979, A341980.

Sequence in context: A357984 A328766 A219203 * A356915 A226786 A266330

Adjacent sequences: A341978 A341979 A341980 * A341982 A341983 A341984

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved