A371213 Number of ordered factorizations of n into factors > 5.

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

Offset: 1

Author

Ilya Gutkovskiy, Mar 15 2024

Keywords

• nonn

Examples

			a(42) = 3: 42 = 6*7 = 7*6.
		

Links

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

Crossrefs

Cf. A002033, A017900, A074206, A185326, A371209, A371211, A371212.

Programs

Mathematica

a[n_] := a[n] = If[n == 1, n, Sum[If[n/d > 5, a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 96}]

PARI

memoA371213 = Map();
A371213(n) = if(1==n,1,my(v); if(mapisdefined(memoA371213,n,&v), v, v = sumdiv(n,d,if((n/d)<=5, 0, A371213(d))); mapput(memoA371213,n,v); (v))); \\ Antti Karttunen, Jan 13 2025

Formula

a(1) = 1; a(n) = Sum_{d|n, n/d > 5} a(d).

Extensions

More terms from Antti Karttunen, Jan 13 2025