%I #11 Jun 11 2013 19:32:58
%S 1,2,10,185,370,3145,6290,40885,53465,63750,81770,106930,241400,
%T 348750,427720,828750,866200,1207000,1306875,1635449,2613750,3138200,
%U 3270898,7149375,8054345,8177245,14298750,14725400,15691000,16108690,16354490,16989375,30368120
%N Numbers n such that sum(d|n, sigma(d)^2) is a multiple of n.
%H Giovanni Resta, <a href="/A226563/b226563.txt">Table of n, a(n) for n = 1..71</a> (terms < 2*10^9)
%e Divisors of 3145 are 1, 5, 17, 37, 85, 185, 629, 3145.
%e sigma(1) = 1, sigma(5) = 6, sigma(17) = 18, sigma(37) = 38, sigma(85) = 108, sigma(185) = 228, sigma(629) = 684, sigma(3145) = 4104.
%e (1^2 + 6^2 + 18^2 + 38^2 + 108^2 + 228^2 + 684^2 + 4104^2) / 3145 = 5525.
%p with(numtheory); ListA226563:=proc(q) local a,b,k,n;
%p for n from 1 to q do a:=[op(divisors(n))]; b:=add(sigma(a[k])^2,k=1..nops(a));
%p if type(b/n,integer) then print(n); fi; od; end: ListA226563(10^6);
%Y Cf. A068978, A068986, A226564-A226566
%K nonn
%O 1,2
%A _Paolo P. Lava_, Jun 11 2013
%E a(14)-a(33) from _Giovanni Resta_, Jun 11 2013