A226563 Numbers k such that sum(d|k, sigma(d)^2) is a multiple of k.

1, 2, 10, 185, 370, 3145, 6290, 40885, 53465, 63750, 81770, 106930, 241400, 348750, 427720, 828750, 866200, 1207000, 1306875, 1635449, 2613750, 3138200, 3270898, 7149375, 8054345, 8177245, 14298750, 14725400, 15691000, 16108690, 16354490, 16989375, 30368120

Offset: 1

Author

Paolo P. Lava, Jun 11 2013

Keywords

• nonn

Examples

			Divisors of 3145 are 1, 5, 17, 37, 85, 185, 629, 3145.
sigma(1) = 1, sigma(5) = 6, sigma(17) = 18, sigma(37) = 38, sigma(85) = 108, sigma(185) = 228, sigma(629) = 684, sigma(3145) = 4104.
(1^2 + 6^2 + 18^2 + 38^2 + 108^2 + 228^2 + 684^2 + 4104^2) / 3145 = 5525.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..71 (terms < 2*10^9)

Crossrefs

Cf. A068978, A068986, A226564-A226566

Programs

Maple

with(numtheory); ListA226563:=proc(q) local a,b,k,n;
for n from 1 to q do a:=[op(divisors(n))]; b:=add(sigma(a[k])^2,k=1..nops(a));
if type(b/n,integer) then print(n); fi; od; end: ListA226563(10^6);

Extensions

a(14)-a(33) from Giovanni Resta, Jun 11 2013