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A331752 Numbers k such that squarefree part of sigma(k) is equal to squarefree part of 2*k.

%I A331752 #33 Jul 03 2021 07:17:42
%S A331752 6,28,468,496,775,2268,3780,4655,7448,8128,9000,10880,10976,25137,
%T A331752 40131,40176,58752,62775,66960,91000,137541,137940,140800,160930,
%U A331752 167400,173600,195938,224450,307125,377055,399360,406224,417477,494832,569184,603288,634725,639158,658368,773175,869022,881280,889056,1005480
%N A331752 Numbers k such that squarefree part of sigma(k) is equal to squarefree part of 2*k.
%C A331752 Numbers k such that A007913(sigma(k)) is equal to A007913(2*k), thus numbers for which sigma(k) has the same set of distinct prime factors with an odd exponent as 2*k.
%C A331752 Among the first 257 terms, these four are also in A228058:
%C A331752   46277101  = 61 * 13^2 * 67^2,
%C A331752   49889853  = 13 * 3^2 * 653^2,
%C A331752   106706925 = 13 * 3^2 * 5^2 * 191^2,
%C A331752   676830973 = 37 * 7^2 * 13^2 * 47^2.
%H A331752 Antti Karttunen, <a href="/A331752/b331752.txt">Table of n, a(n) for n = 1..257</a>
%H A331752 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%e A331752 For n = 46277101 = 61 * 13^2 * 67^2, sigma(46277101) = 51703722 = 2 * 3^2 * 7^2 * 31^2 * 61, with A007913(sigma(46277101)) = 2*61 = A007913(2*46277101), thus 46277101 is included in this sequence.
%t A331752 Select[Range[10^6], SameQ @@ Map[Sqrt[#] /. (c_: 1)*a_^(b_: 0) :> (c*a^b)^2 &, {DivisorSigma[1, #], 2 #}] &] (* _Michael De Vlieger_, Feb 08 2020, after _Bill Gosper_ at A007913 *)
%o A331752 (PARI) isA331752(n) = (core(2*n)==core(sigma(n)));
%Y A331752 Cf. A000203, A006532, A007913, A228058, A331751, A332208.
%Y A331752 Cf. A000396 (a subsequence).
%K A331752 nonn
%O A331752 1,1
%A A331752 _Antti Karttunen_, Feb 06 2020