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

1,2

Comments

Subset of A020477.

Links

Table of n, a(n) for n=1..33.

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A217331 A284448 A274252 * A030512 A097725 A353142

Adjacent sequences: A303990 A303991 A303992 * A303994 A303995 A303996

Keyword

nonn,easy

Author

Paolo P. Lava, May 04 2018

Status

approved