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