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A304650 Number of ways to write n as a product of two positive integers, neither of which is a perfect power. 1
0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2, 0, 6, 0, 0, 2, 2, 2, 5, 0, 2, 2, 2, 0, 6, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 8, 0, 2, 2, 0, 2, 6, 0, 2, 2, 6, 0, 4, 0, 2, 2, 2, 2, 6, 0, 2, 0, 2, 0, 8, 2, 2, 2, 2, 0, 8, 2, 2, 2, 2, 2, 2, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..98.

EXAMPLE

The a(60) = 8 ways to write 60 as a product of two numbers, neither of which is a perfect power, are 2*30, 3*20, 5*12, 6*10, 10*6, 12*5, 20*3, 30*2.

MATHEMATICA

radQ[n_]:=And[n>1, GCD@@FactorInteger[n][[All, 2]]===1];

Table[Length[Select[Divisors[n], radQ[#]&&radQ[n/#]&]], {n, 100}]

PROG

(PARI) ispow(n) = (n==1) || ispower(n);

a(n) = sumdiv(n, d, !ispow(d) && !ispow(n/d)); \\ Michel Marcus, May 17 2018

CROSSREFS

Cf. A000005, A001055, A007427, A007916, A034444, A045778, A162247, A183096, A281116, A301700, A303386, A303707, A304649.

Sequence in context: A025867 A078646 A264405 * A347992 A317581 A035217

Adjacent sequences:  A304647 A304648 A304649 * A304651 A304652 A304653

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 15 2018

STATUS

approved

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Last modified October 2 23:51 EDT 2022. Contains 357230 sequences. (Running on oeis4.)