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

1,36

Links

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

Formula

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

Example

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

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}]

Prog

(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

Crossrefs

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

Sequence in context: A360119 A033630 A308608 * A378604 A323719 A220122

Adjacent sequences: A371210 A371211 A371212 * A371214 A371215 A371216

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 15 2024

Extensions

More terms from Antti Karttunen, Jan 13 2025

Status

approved