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A295923 Number of twice-factorizations of n where the first factorization is constant, i.e., type (P,R,P). 7
1, 1, 1, 3, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 2, 10, 1, 4, 1, 4, 2, 2, 1, 7, 3, 2, 4, 4, 1, 5, 1, 8, 2, 2, 2, 13, 1, 2, 2, 7, 1, 5, 1, 4, 4, 2, 1, 12, 3, 4, 2, 4, 1, 7, 2, 7, 2, 2, 1, 11, 1, 2, 4, 29, 2, 5, 1, 4, 2, 5, 1, 16, 1, 2, 4, 4, 2, 5, 1, 12, 10, 2, 1, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) is also the number of ways to choose a perfect divisor d|n and then a sequence of log_d(n) factorizations of d.

LINKS

Table of n, a(n) for n=1..84.

EXAMPLE

The a(16) = 10 twice-factorizations are (2*2*2*2), (2*2*4), (2*8), (4*4), (16), (2*2)*(2*2), (2*2)*(4), (4)*(2*2), (4)*(4), (2)*(2)*(2)*(2).

MATHEMATICA

postfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[postfacs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];

a[n_]:=Sum[Length[postfacs[n^(1/g)]]^g, {g, Divisors[GCD@@FactorInteger[n][[All, 2]]]}];

Array[a, 50]

CROSSREFS

Cf. A000005, A001055, A052409, A052410, A279787, A281113, A284639, A295920, A295924, A295931, A295935.

Sequence in context: A046645 A284639 A320887 * A325806 A016470 A059807

Adjacent sequences:  A295920 A295921 A295922 * A295924 A295925 A295926

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 30 2017

STATUS

approved

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Last modified August 10 02:28 EDT 2020. Contains 336367 sequences. (Running on oeis4.)