Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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