OFFSET
1,4
COMMENTS
Terms in this sequence only depend on the prime signature of n. - David A. Corneth, Dec 26 2018
LINKS
EXAMPLE
The a(144) = 13 factorizations:
(144),
(4*36), (9*16),
(2*2*36), (2*8*9), (3*3*16), (4*4*9),
(2*2*4*9), (2*3*3*8), (3*3*4*4),
(2*2*2*2*9), (2*2*3*3*4),
(2*2*2*2*3*3).
MATHEMATICA
perpowQ[n_]:=GCD@@FactorInteger[n][[All, 2]]>1;
pfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[pfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], Or[PrimeQ[#], perpowQ[#]]&]}]];
Table[Length[pfacs[n]], {n, 100}]
PROG
(PARI) A322453(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&(ispower(d)||isprime(d)), s += A322453(n/d, d))); (s)); \\ Antti Karttunen, Dec 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 09 2018
EXTENSIONS
More terms from Antti Karttunen, Dec 24 2018
STATUS
approved