OFFSET
1,36
COMMENTS
The characteristic function of nonzero terms is A065043. - R. J. Mathar, Jan 18 2021
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
EXAMPLE
The a(900) = 5 factorizations into semiprimes:
900 = (4*9*25)
900 = (4*15*15)
900 = (6*6*25)
900 = (6*10*15)
900 = (9*10*10)
The a(900) = 5 multiset partitions into pairs:
{{1,1},{2,2},{3,3}}
{{1,1},{2,3},{2,3}}
{{1,2},{1,2},{3,3}}
{{1,2},{1,3},{2,3}}
{{2,2},{1,3},{1,3}}
MATHEMATICA
semfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[semfacs[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], PrimeOmega[#]==2&]}]];
Table[Length[semfacs[n]], {n, 100}]
PROG
(PARI) A320655(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((2==bigomega(d)&&(d<=m)), s += A320655(n/d, d))); (s)); \\ Antti Karttunen, Dec 06 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 18 2018
EXTENSIONS
Data section extended up to 105 terms by Antti Karttunen, Dec 06 2020
STATUS
approved