OFFSET
1,2
COMMENTS
Subset of A006532.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..111 (terms < 10^9)
EXAMPLE
Divisors of 66 are 1, 2, 3, 6, 11, 22, 33, 66 and sigma(66) = 144. Then:
144 / 1 = 144, 144 / 2 = 72, 144 / 3 = 48, 144 / 6 = 24 and (1 + 2 + 3 + 6)^2 = 12^2 = 144.
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^2=sigma(n) then print(n); fi; od; end: P(10^9);
MATHEMATICA
Select[Range[10^5], (d = DivisorSigma[1, #]; IntegerQ@ Sqrt@ d && d == DivisorSigma[1, GCD[d, #]]^2) &] (* Giovanni Resta, Mar 28 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 24 2017
EXTENSIONS
a(1) and a(32) from Giovanni Resta, Mar 28 2017
STATUS
approved