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

1,2

Comments

Subset of A019422.

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000203, A019422, A303123, A303993, A303995, A303996.

Sequence in context: A071687 A345361 A048254 * A249551 A248790 A252877

Adjacent sequences: A303991 A303992 A303993 * A303995 A303996 A303997

Keyword

nonn

Author

Paolo P. Lava, May 04 2018

Extensions

More terms from Michel Marcus, May 05 2018

Status

approved