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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).
2
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
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
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 24 2017
EXTENSIONS
a(1), a(25)-a(33) from Giovanni Resta, Mar 28 2017
STATUS
approved