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%I #16 Mar 28 2017 08:16:28
%S 1,66,1092,1416,38280,38760,43080,92960,101024,112672,168210,175230,
%T 180090,194130,260400,491536,863772,891996,1004640,1061400,1234464,
%U 1282848,1294944,2010528,2041632,2079648,2090016,3394440,3653640,3673080,3701160,5528250
%N Let x be the sum of the divisors d_i of k such that d_i | sigma(k). Sequence lists the numbers k for which x^2 = sigma(k).
%C Subset of A006532.
%H Giovanni Resta, <a href="/A284283/b284283.txt">Table of n, a(n) for n = 1..111</a> (terms < 10^9)
%e Divisors of 66 are 1, 2, 3, 6, 11, 22, 33, 66 and sigma(66) = 144. Then:
%e 144 / 1 = 144, 144 / 2 = 72, 144 / 3 = 48, 144 / 6 = 24 and (1 + 2 + 3 + 6)^2 = 12^2 = 144.
%p with(numtheory): P:=proc(q) local a,k,n,x;
%p for n from 1 to q do a:=sort([op(divisors(n))]); x:=0;
%p for k from 1 to nops(a)-1 do if type(sigma(n)/a[k],integer) then x:=x+a[k]; fi; od;
%p if x^2=sigma(n) then print(n); fi; od; end: P(10^9);
%t Select[Range[10^5], (d = DivisorSigma[1, #]; IntegerQ@ Sqrt@ d && d == DivisorSigma[1, GCD[d, #]]^2) &] (* _Giovanni Resta_, Mar 28 2017 *)
%Y Cf. A000203, A006532, A284284.
%K nonn
%O 1,2
%A _Paolo P. Lava_, Mar 24 2017
%E a(1) and a(32) from _Giovanni Resta_, Mar 28 2017
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