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Numbers n such that sum(d|n, sigma(d)^2/d) is an integer, where d are the divisors of n.
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%I #8 Jun 11 2013 20:10:34

%S 1,205,3895,8525,17050,71951,74005,148010,359755,451825,903650,

%T 1628110,1632005,1798775,2346674,3597550,4218285,8436570,8993875,

%U 14749955,17987750,50471410,59071771,92802270,95335075,190670150,280249145,295358855,451356495,481068170

%N Numbers n such that sum(d|n, sigma(d)^2/d) is an integer, where d are the divisors of n.

%H Giovanni Resta, <a href="/A226564/b226564.txt">Table of n, a(n) for n = 1..34</a> (terms < 2*10^9)

%e Divisors of 71951 are 1, 11, 31, 211, 341, 2321, 6541, 71951.

%e sigma(1) = 1, sigma(11) = 12, sigma(31) = 32, sigma(211) = 212, sigma(341) = 384, sigma(2321) = 2544, sigma(6541) = 6784, sigma(71951) = 81408.

%e (1^2/1 + 12^2/11 + 32^2/31 + 212^2/211 + 384^2/341 + 2544^2/2321 + 6784^2/6541 + 81408^2/71951) = 102625.

%p with(numtheory); ListA226564:=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/a[k],k=1..nops(a));

%p if type(b,integer) then print(n); fi; od; end: ListA226564(10^6);

%Y Cf. A068978, A068986, A226563, A226564, A226566

%K nonn

%O 1,2

%A _Paolo P. Lava_, Jun 11 2013

%E a(12)-a(30) from _Giovanni Resta_, Jun 11 2013