A371244 Number of factorizations of n into factors > 3.

1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 3, 1, 2, 1, 2, 2, 1, 1, 3, 2, 2, 1, 2, 1, 2, 2, 3, 1, 1, 1, 4, 1, 1, 2, 4, 2, 2, 1, 2, 1, 3, 1, 4, 1, 1, 2, 2, 2, 2, 1, 5, 2, 1, 1, 4, 2, 1, 1, 3, 1, 4, 2, 2, 1, 1, 2, 5, 1, 2, 2, 5, 1, 2, 1, 3, 3, 1, 1, 4

Offset: 1

Author

Ilya Gutkovskiy, Mar 16 2024

Keywords

• nonn

Examples

			a(36) = 3: 36 = 4*9 = 6*6.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001055, A008484, A017898, A371211, A371243, A371245.

Programs

PARI

A371244(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>3)&&(d<=m), s += A371244(n/d, d))); (s)); \\ Antti Karttunen, Jan 16 2025

Formula

Dirichlet g.f.: Product_{k>=4} 1 / (1 - k^(-s)).

Extensions

More terms from Antti Karttunen, Jan 16 2025