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 A320655 Number of factorizations of n into semiprimes. Number of multiset partitions of the multiset of prime factors of n, into pairs. 59
 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 1, 0, 1, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 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 The positions of zeros are A026424. Cf. A001055, A001222, A001358, A007716, A007717, A056239, A112798, A318871, A318953, A320462, A320656, A320658, A320659. Sequence in context: A269953 A326411 A309163 * A277017 A178498 A095408 Adjacent sequences:  A320652 A320653 A320654 * A320656 A320657 A320658 KEYWORD nonn AUTHOR Gus Wiseman, Oct 18 2018 EXTENSIONS Data section extended up to 105 terms by Antti Karttunen, Dec 06 2020 STATUS approved

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Last modified July 28 15:51 EDT 2021. Contains 346335 sequences. (Running on oeis4.)