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Numbers k such that sigma(core(k)) = tau(k) where core(k) is the squarefree part of k, tau(k) is the number of divisors of k, and sigma(k) is their sum.
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%I #15 Jul 11 2019 10:09:34

%S 1,20,27,45,96,150,245,294,486,504,540,605,612,726,832,845,1014,1400,

%T 1445,1500,1700,1734,1805,2166,2645,3125,3168,3174,3332,3825,4176,

%U 4205,4352,4805,4950,5046,5324,5766,6174,6615,6776,6845,7497,8214,8228,8405

%N Numbers k such that sigma(core(k)) = tau(k) where core(k) is the squarefree part of k, tau(k) is the number of divisors of k, and sigma(k) is their sum.

%H Amiram Eldar, <a href="/A069827/b069827.txt">Table of n, a(n) for n = 1..10000</a>

%t core[n_] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 2]} & /@ FactorInteger[n]); Select[Range[10^5], DivisorSigma[0, #] == DivisorSigma[1, core[#]] &] (* _Amiram Eldar_, Jul 11 2019 after Zak Seidov at A007913 *)

%o (PARI) isok(n) = sigma(core(n)) == numdiv(n); \\ _Michel Marcus_, Aug 09 2013

%Y Cf. A000005, A000203, A007913.

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Apr 28 2002