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 A316978 Number of factorizations of n into factors > 1 with no equivalent primes. 29
 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 4, 1, 1, 1, 5, 1, 4, 1, 4, 1, 1, 1, 7, 2, 1, 3, 4, 1, 1, 1, 7, 1, 1, 1, 7, 1, 1, 1, 7, 1, 1, 1, 4, 4, 1, 1, 12, 2, 4, 1, 4, 1, 7, 1, 7, 1, 1, 1, 7, 1, 1, 4, 11, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 4, 4, 1, 1, 1, 12, 5, 1, 1, 7, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS In a factorization, two primes are equivalent if each factor has in its prime factorization the same multiplicity of both primes. LINKS FORMULA a(prime^n) = A000041(n). a(squarefree) = 1. EXAMPLE The a(36) = 7 factorizations are (2*2*3*3), (2*2*9), (2*3*6), (3*3*4), (2*18), (3*12), (4*9). Missing from this list are (6*6) and (36). MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}]; Table[Length[Select[facs[n], UnsameQ@@dual[primeMS/@#]&]], {n, 100}] CROSSREFS Cf. A001055, A007716, A007717, A020555, A045778, A162247, A281116, A303386. Cf. A316974, A316979, A316980, A316981. Sequence in context: A325939 A318586 A222580 * A331023 A284345 A183214 Adjacent sequences:  A316975 A316976 A316977 * A316979 A316980 A316981 KEYWORD nonn AUTHOR Gus Wiseman, Jul 18 2018 STATUS approved

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Last modified February 18 03:40 EST 2020. Contains 332006 sequences. (Running on oeis4.)