A284284 Let x be the sum of the divisors d_i of k such that d_i | sigma(k). Sequence lists the numbers k for which x^3 = sigma(k).

1, 690, 714, 75432, 81172, 81192, 81624, 82248, 84196, 305320, 312040, 315880, 619542, 639198, 646758, 665874, 684342, 737694, 743958, 750114, 751626, 761454, 762966, 763614, 4349280, 4651680, 4789920, 4939680, 4981920, 5259936, 5325216, 5428896, 5474976

Offset

1,2

Comments

Subset of A020477.

Links

Giovanni Resta, Table of n, a(n) for n = 1..200

Example

Divisors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690 and sigma(690) = 1728. Then:
1728 / 1 = 1728, 1728 / 2 = 864, 1728 /  3 = 576, 1728 / 6 = 288 and (1 + 2 + 3 + 6)^2 = 12^3 = 1728.

Maple

with(numtheory): P:=proc(q) local a, k, n, x;
for n from 1 to q do a:=sort([op(divisors(n))]); x:=0;
for k from 1 to nops(a)-1 do if type(sigma(n)/a[k], integer) then x:=x+a[k]; fi; od;
if x^3=sigma(n) then print(n); fi; od; end: P(10^6);

Mathematica

Select[Range[10^5], (d = DivisorSigma[1, #]; IntegerQ[ d^(1/3)] && d == DivisorSigma[1, GCD[d, #]]^3) &] (* Giovanni Resta, Mar 28 2017 *)

Crossrefs

Cf. A000203, A020477, A284283.

Sequence in context: A259512 A078877 A204145 * A115177 A263114 A214335

Adjacent sequences: A284281 A284282 A284283 * A284285 A284286 A284287

Keyword

nonn

Author

Paolo P. Lava, Mar 24 2017

Extensions

a(1), a(25)-a(33) from Giovanni Resta, Mar 28 2017

Status

approved