

A303995


Numbers whose sum of divisors is the fifth power of one of their divisors.


6



1, 3210, 3498, 3882, 6453804, 7873684, 7943640, 8028120, 8099880, 9112230, 9561990, 10079430, 182626920, 192651480, 196192920, 199939320, 200271960, 201632760, 203289240, 206367480, 206645880, 207815160, 208955160, 210368760, 210406680, 210717720, 211645560
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OFFSET

1,2


COMMENTS



LINKS



EXAMPLE

Divisors of 3210 are 1, 2, 3, 5, 6, 10, 15, 30, 107, 214, 321, 535, 642, 1070, 1605, 3210 and their sum is 7776 = 6^5.


MAPLE

with(numtheory): P:=proc(q) local a, k, n;
for n from 1 to q do a:=sort([op(divisors(n))]);
for k from 1 to nops(a) do if sigma(n)=a[k]^5 then print(n); break; fi; od; od; end: P(10^9);


MATHEMATICA

Select[Range[10^4], IntegerQ[t = DivisorSigma[1, #]^(1/5)] && Mod[#, t] == 0 &] (* Giovanni Resta, May 04 2018 *)


PROG

(PARI) isok(n) = (n==1)  (ispower(s=sigma(n), 5) && !(n % sqrtnint(s, 5))); \\ Michel Marcus, May 05 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



