A048946 Numbers k such that the product of divisors of k is a fifth power.

1, 16, 32, 48, 80, 81, 112, 144, 162, 176, 208, 240, 243, 272, 304, 324, 336, 368, 400, 405, 432, 464, 496, 512, 528, 560, 567, 592, 624, 625, 648, 656, 688, 720, 752, 784, 810, 816, 848, 880, 891, 912, 944, 976, 1008, 1024, 1040, 1053, 1072, 1104, 1134

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Divisor Product

Mathematica

Select[Range[1135], IntegerQ@ Power[Times @@ Divisors[#], 1/5] &] (* Michael De Vlieger, Mar 09 2022 *)

Prog

(PARI) is(n)=ispower(n, 5) || numdiv(n)%5==0 \\ Charles R Greathouse IV, May 25 2011
(Magma) A048946:=func< n | IsPower(&*Divisors(n), 5) >; [ n: n in [1..1134] | A048946(n) ];  // Bruno Berselli, May 25 2011

Crossrefs

Cf. A007955 (product of divisors of n), A000584 (5th powers).

Sequence in context: A023707 A044442 A082294 * A260050 A224544 A255994

Adjacent sequences: A048943 A048944 A048945 * A048947 A048948 A048949

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved