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 A319786 Number of factorizations of n where no two factors are relatively prime. 9
 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 5, 1, 2, 1, 2, 1, 1, 1, 4, 2, 1, 3, 2, 1, 1, 1, 7, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 7, 2, 2, 1, 2, 1, 4, 1, 4, 1, 1, 1, 3, 1, 1, 2, 11, 1, 1, 1, 2, 1, 1, 1, 7, 1, 1, 2, 2, 1, 1, 1, 7, 5, 1, 1, 3, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 12, 1, 2, 2, 4, 1, 1, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS First differs from A305193 at a(36) = 4, A305193(36) = 5. a(n) depends only on prime signature of n (cf. A025487). - Antti Karttunen, Nov 07 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 1..11520 Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000 EXAMPLE The a(48) = 7 factorizations are (2*2*2*6), (2*2*12), (2*4*6), (2*24), (4*12), (6*8), (48). MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Length[Select[facs[n], !Or@@CoprimeQ@@@Subsets[#, {2}]&]], {n, 100}] PROG (PARI) A319786(n, m=n, facs=List([])) = if(1==n, (1!=gcd(Vec(facs))), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs, d); s += A319786(n/d, d, newfacs))); (s)); \\ Antti Karttunen, Nov 07 2018 CROSSREFS Cf. A001055, A007716, A045778, A049311, A162247, A281116, A283877, A305193, A305854, A306006, A316980, A318749. Cf. A319755, A319759, A319760, A319765, A319779, A319787, A319782, A319789. Sequence in context: A327012 A328855 A327658 * A321271 A305193 A038538 Adjacent sequences:  A319783 A319784 A319785 * A319787 A319788 A319789 KEYWORD nonn AUTHOR Gus Wiseman, Sep 27 2018 EXTENSIONS More terms from Antti Karttunen, Nov 07 2018 STATUS approved

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Last modified July 31 23:46 EDT 2021. Contains 346377 sequences. (Running on oeis4.)