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A252234 Numbers n such that there exists an m so that squarefree kernel of n = squarefree kernel of m, and n is the sum of the proper divisors of m (m may equal n).

%I A252234 #42 Mar 02 2018 02:11:09
%S A252234 6,28,36,50,240,312,384,450,496,810,1008,1344,4256,4536,8128,10800,
%T A252234 11700,14112,15288,19656,23040,49686,90720,95040,98280,98553,124848,
%U A252234 129024,153760,249018,256932,260100,378225,404586,454860,532224,561834,700245,714240
%N A252234 Numbers n such that there exists an m so that squarefree kernel of n = squarefree kernel of m, and n is the sum of the proper divisors of m (m may equal n).
%C A252234 Since m=n is allowed, perfect numbers (A000396) are terms of this sequence. - _Michel Marcus_, Jan 02 2015
%C A252234 m: 6, 24, 28, 40, 120, 216, 234, 270, 360, 496, 588, 672, 2016, ..., . - _Robert G. Wilson v_, Feb 28 2015
%C A252234 Odd members are 98553, 378225, 700245, ..., . - _Robert G. Wilson v_, Feb 28 2015
%H A252234 Robert G. Wilson v, <a href="/A252234/b252234.txt">Table of n, a(n) for n = 1..157</a>
%H A252234 Robert G. Wilson v, <a href="/A252234/a252234.txt">Table of n, a(n) and m for n = 1..157</a>
%e A252234 For n = 36, m = 24, 36 is the sum of the proper divisors of 24, and rad(36) = rad(24) = 6.
%t A252234 rad[n_] := Times @@ (First@ # & /@ FactorInteger@ n); f[n_] := Block[{sd = DivisorSigma[1, n] - n}, If[ rad[n] == rad[sd], sd, 0]]; k = 1; lst = {}; While[k < 1000001, a = f@ k; If[a > 0, AppendTo[lst, a]]; k++]; Sort@ lst (* _Robert G. Wilson v_, Feb 28 2015 *)
%Y A252234 Cf. A001065 (sum of proper divisors of n), A007947 (the squarefree kernel of n).
%Y A252234 Cf. A048138, A152454, A252997.
%K A252234 nonn
%O A252234 1,1
%A A252234 _Naohiro Nomoto_, Dec 15 2014