A371212 Number of ordered factorizations of n into factors > 4.

1, 0, 0, 0, 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, 3, 1, 1, 1, 1, 3, 2, 1, 1, 1, 3, 1, 3, 1, 1, 3, 1, 1, 3, 2, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 5, 1, 1, 3, 2, 3, 3, 1, 1, 1, 5, 1, 5, 1, 1, 3, 1, 3, 3, 1, 5, 2, 1, 1, 5, 3, 1, 1, 3, 1, 7, 3, 1, 1, 1, 3, 5, 1, 3, 3, 4, 1, 3, 1, 3, 5, 1, 1, 5

Offset: 1

Author

Ilya Gutkovskiy, Mar 15 2024

Keywords

• nonn

Examples

			a(30) = 3: 30 = 5*6 = 6*5.
		

Links

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

Crossrefs

Cf. A002033, A017899, A074206, A185325, A371209, A371211, A371213.

Programs

Mathematica

a[n_] := a[n] = If[n == 1, n, Sum[If[n/d > 4, a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 92}]

PARI

memoA371212 = Map();
A371212(n) = if(1==n,1,my(v); if(mapisdefined(memoA371212,n,&v), v, v = sumdiv(n,d,if((n/d)<=4, 0, A371212(d))); mapput(memoA371212,n,v); (v))); \\ Antti Karttunen, Jan 16 2025

Formula

a(1) = 1; a(n) = Sum_{d|n, n/d > 4} a(d).

Extensions

More terms from Antti Karttunen, Jan 16 2025