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A296132 Number of twice-factorizations of n where the first factorization is constant and the latter factorizations are strict, i.e., type (P,R,Q). 1
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 5, 2, 2, 3, 3, 1, 5, 1, 4, 2, 2, 2, 9, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 7, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 9, 1, 2, 3, 10, 2, 5, 1, 3, 2, 5, 1, 9, 1, 2, 3, 3, 2, 5, 1, 7, 4, 2, 1, 9, 2, 2, 2 (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) strict factorizations of d.

LINKS

Table of n, a(n) for n=1..87.

EXAMPLE

The a(36) = 9 twice-factorizations are (2*3)*(2*3), (2*3)*(6), (6)*(2*3), (6)*(6), (2*3*6), (2*18), (3*12), (4*9), (36).

MATHEMATICA

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

Table[Sum[Length[sfs[n^(1/g)]]^g, {g, Divisors[GCD@@FactorInteger[n][[All, 2]]]}], {n, 100}]

CROSSREFS

Cf. A000005, A001055, A005117, A045778, A052409, A052410, A089723, A279788, A281113, A284639, A295920, A295931.

Sequence in context: A086436 A001222 A257091 * A253557 A098893 A069248

Adjacent sequences:  A296128 A296129 A296131 * A296133 A296134 A296136

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 05 2017

STATUS

approved

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Last modified January 18 18:45 EST 2018. Contains 297864 sequences.