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A301829 Number of ways to choose a nonempty submultiset of a factorization of n into factors greater than one. 7
0, 1, 1, 3, 1, 4, 1, 7, 3, 4, 1, 12, 1, 4, 4, 15, 1, 12, 1, 12, 4, 4, 1, 29, 3, 4, 7, 12, 1, 17, 1, 29, 4, 4, 4, 37, 1, 4, 4, 29, 1, 17, 1, 12, 12, 4, 1, 64, 3, 12, 4, 12, 1, 29, 4, 29, 4, 4, 1, 53, 1, 4, 12, 54, 4, 17, 1, 12, 4, 17, 1, 92, 1, 4, 12, 12, 4, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..78.

FORMULA

a(n) = Sum_{d|n, d>1} f(d) * f(n/d) where f(n) = A001055(n) is the number of factorizations of n into factors greater than 1.

EXAMPLE

The a(12) = 12 submultisets ("<" means subset or equal):

(2)<(2*2*3), (3)<(2*2*3), (2*2)<(2*2*3), (2*3)<(2*2*3), (2*2*3)<(2*2*3),

(2)<(2*6), (6)<(2*6), (2*6)<(2*6),

(3)<(3*4), (4)<(3*4), (3*4)<(3*4),

(12)<(12).

MATHEMATICA

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

Table[Sum[Length[facs[d]]*Length[facs[n/d]], {d, Rest[Divisors[n]]}], {n, 100}]

CROSSREFS

Cf. A000712, A001055, A001222, A001405, A122768, A276024, A281113, A284640, A295632, A299701, A299702, A299729, A301830.

Sequence in context: A210622 A295276 A301856 * A006022 A078896 A322582

Adjacent sequences:  A301826 A301827 A301828 * A301830 A301831 A301832

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 27 2018

STATUS

approved

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Last modified February 23 08:18 EST 2019. Contains 320420 sequences. (Running on oeis4.)