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 A327525 Number of factorizations of A302569(n), the n-th number that is 1, prime, or whose prime indices are pairwise coprime. 0
 1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 4, 1, 2, 2, 5, 1, 1, 4, 2, 1, 7, 2, 4, 1, 5, 1, 7, 2, 2, 2, 1, 2, 7, 1, 1, 4, 2, 1, 12, 2, 4, 1, 2, 7, 2, 1, 11, 1, 2, 11, 5, 1, 4, 2, 5, 1, 1, 2, 4, 2, 1, 12, 2, 1, 2, 2, 7, 1, 4, 2, 2, 2, 19, 1, 1, 5, 1, 7, 2, 1, 1, 5, 12, 1, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. LINKS FORMULA a(n) = A001055(A302569(n)). EXAMPLE The a(47) = 11 factorizations of 60 together with the corresponding multiset partitions of {1,1,2,3}:   (2*2*3*5)  {{1},{1},{2},{3}}   (2*2*15)   {{1},{1},{2,3}}   (2*3*10)   {{1},{2},{1,3}}   (2*5*6)    {{1},{3},{1,2}}   (2*30)     {{1},{1,2,3}}   (3*4*5)    {{2},{1,1},{3}}   (3*20)     {{2},{1,1,3}}   (4*15)     {{1,1},{2,3}}   (5*12)     {{3},{1,1,2}}   (6*10)     {{1,2},{1,3}}   (60)       {{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, #]&]}]]; primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; y=Select[Range[nn], PrimeQ[#]||CoprimeQ@@primeMS[#]&]; Table[Length[facsusing[Rest[y], n]], {n, y}] CROSSREFS See link for additional cross-references. Cf. A056239, A112798, A281116, A318721, A302569, A304711, A305079. Sequence in context: A134583 A087467 A231568 * A327540 A227687 A128118 Adjacent sequences:  A327522 A327523 A327524 * A327526 A327527 A327528 KEYWORD nonn AUTHOR Gus Wiseman, Sep 20 2019 STATUS approved

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)