A303993 Numbers whose sum of divisors is the cube of one of their divisors.

1, 102, 8148, 63720, 66120, 71880, 196896, 446040, 452760, 462840, 471960, 503160, 517320, 544920, 549240, 554280, 559320, 575880, 756400, 1458912, 1499232, 1579872, 1634040, 1659960, 1748520, 5294800, 9740640, 10103520, 11103456, 11438280, 11583264, 11619720, 11915640

Offset: 1

Author

Paolo P. Lava, May 04 2018

Keywords

• nonn
• easy

Comments

Subset of A020477.

Examples

			Divisors of 102 are 1, 2, 3, 6, 17, 34, 51, 102 and their sum is 216 = 6^3.
		

Crossrefs

Cf. A000203, A020477, A303123, A303994, A303995, A303996.

Programs

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]^3 then print(n); break; fi; od; od; end: P(10^9);

Mathematica

Select[Range[10^6], Mod[#, DivisorSigma[1, #]^(1/3)] == 0 &] (* Michael De Vlieger, May 06 2018 *)

PARI

isok(n) = (n==1) || (ispower(s=sigma(n), 3) && !(n % sqrtnint(s, 3))); \\ Michel Marcus, May 05 2018