A303994 Numbers whose sum of divisors is the fourth power of one of their divisors.

1, 510, 642, 3394440, 3629640, 3653640, 3663240, 3673080, 3701160, 3736920, 3901080, 3958680, 4077960, 4137240, 4240920, 4251480, 4256520, 4273320, 4274520, 4319880, 7300854, 12798240, 13362720, 14405664, 15170820, 16173024, 16342368, 16354884, 16361184, 16957668, 17113404

Offset: 1

Author

Paolo P. Lava, May 04 2018

Keywords

• nonn

Comments

Subset of A019422.

Examples

			Divisors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510 and their sum is 1296 = 6^4.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1565 (terms < 10^12; first 398 terms from Robert Israel)

Crossrefs

Cf. A000203, A019422, A303123, A303993, 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]^4 then print(n); break; fi; od; od; end: P(10^9);

Mathematica

Select[Range[17114000],MemberQ[Divisors[#]^4,DivisorSigma[1,#]]&] (* Harvey P. Dale, Jul 22 2021 *)

PARI

isok(n) = (n==1) || (ispower(s=sigma(n), 4) && !(n % sqrtnint(s, 4))); \\ Michel Marcus, May 05 2018

Extensions

More terms from Michel Marcus, May 05 2018