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 A327518 Number of factorizations of A302696(n), the n-th number that is 1, 2, or a nonprime number with pairwise coprime prime indices, into factors > 1 satisfying the same conditions. 0
 1, 1, 2, 1, 3, 1, 2, 1, 1, 5, 2, 1, 4, 1, 2, 2, 7, 1, 1, 1, 1, 4, 2, 1, 7, 1, 2, 1, 4, 1, 5, 1, 11, 2, 2, 1, 2, 1, 2, 1, 7, 1, 1, 1, 4, 2, 1, 1, 1, 12, 2, 4, 1, 2, 7, 2, 1, 1, 10, 1, 1, 2, 15, 5, 1, 4, 2, 5, 1, 1, 1, 1, 1, 2, 4, 2, 1, 1, 12, 1, 2, 1, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS EXAMPLE The a(59) = 10 factorizations of 120 using the allowed factors, together with the corresponding multiset partitions of {1,1,1,2,3}:   (2*2*2*15)  {{1},{1},{1},{2,3}}   (2*2*30)    {{1},{1},{1,2,3}}   (2*4*15)    {{1},{1,1},{2,3}}   (2*6*10)    {{1},{1,2},{1,3}}   (2*60)      {{1},{1,1,2,3}}   (4*30)      {{1,1},{1,2,3}}   (6*20)      {{1,2},{1,1,3}}   (8*15)      {{1,1,1},{2,3}}   (10*12)     {{1,3},{1,1,2}}   (120)       {{1,1,1,2,3}} MATHEMATICA nn=100; facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]]; y=Select[Range[nn], #==1||CoprimeQ@@primeMS[#]&]; Table[Length[facsusing[Rest[y], n]], {n, y}] CROSSREFS See link for additional cross-references. Cf. A001055, A056239, A112798, A302569, A302696, A304711, A305079, A327392. Sequence in context: A119647 A228098 A327533 * A174532 A089242 A185894 Adjacent sequences:  A327515 A327516 A327517 * A327519 A327520 A327521 KEYWORD nonn AUTHOR Gus Wiseman, Sep 19 2019 STATUS approved

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Last modified June 20 13:08 EDT 2021. Contains 345164 sequences. (Running on oeis4.)