A103264 Number of partitions of n into distinct parts prime to 3, 5 and 7.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 8, 8, 9, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 23, 24, 26, 28, 31, 34, 37, 39, 42, 45, 49, 53, 56, 60, 64, 69, 75, 81, 86, 92, 98, 105, 113, 122, 130, 138, 147, 157, 168, 179, 191, 202, 215, 230, 246, 262, 279

Offset: 0

Author

Noureddine Chair, Feb 21 2005

Keywords

• nonn

Examples

			a(19)=5 because 19 = 17 + 2 = 16 + 2 + 1 = 13 + 4 + 2 = 11 + 8.
		

Programs

Maple

series(product((1+x^k)*(1+x^(15*k))*(1+x^(21*k))*(1+x^(35*k)))/((1+x^(3*k))*(1+x^(5*k))*(1+x^(7*k))*(1+x^(105*k))),k=1..100),x=0,100);

Mathematica

CoefficientList[ Series[ Product[(1 + x^k)(1 + x^(15k))(1 + x^(21k))(1 + x^(35k))/((1 + x^(3k))(1 + x^(5k))(1 + x^(7k))(1 + x^(105k))), {k, 100}], {x, 0, 73}], x] (* Robert G. Wilson v, Feb 22 2005 *)

Formula

G.f.: product_{k>0}((1+x^k)*(1+x^(15k))*(1+x^(21k))*(1+x^(35k)))/((1+x^(3k))*(1+x^(5k))*(1+x^(7k))*(1+x^(105k))).

a(n) ~ exp(4*Pi*sqrt(n/105)) / (sqrt(2) * 105^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2015

Extensions

More terms from Robert G. Wilson v, Feb 22 2005