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

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

1,2

Links

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

Example

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.

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);

Crossrefs

Cf. A068978, A068986, A226564-A226566

Sequence in context: A086675 A319607 A057119 * A037267 A177399 A194971

Adjacent sequences: A226560 A226561 A226562 * A226564 A226565 A226566

Keyword

nonn

Author

Paolo P. Lava, Jun 11 2013

Extensions

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

Status

approved