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%I #22 Mar 21 2023 09:22:31
%S 3,5,6,7,11,13,14,15,17,19,21,22,23,27,28,29,30,31,33,35,37,38,39,41,
%T 42,43,45,46,47,51,53,54,55,57,59,60,61,62,63,65,66,67,69,70,71,73,75,
%U 77,78,79,83,84,85,86,87,89,91,92,93,94,95,97,99,101,102
%N Numbers such that numerator(sigma(n)/n) is even and denominator(sigma(n)/n) is odd.
%C a(n) contains odd primes (A065091), odd squarefree semiprimes (A046388), perfect numbers (A000396), and 2n-multiperfect (A027687, A046061).
%H Vincenzo Librandi, <a href="/A216782/b216782.txt">Table of n, a(n) for n = 1..8000</a>
%e sigma(3)/3 = 4/3 (even/odd).
%t Select[Range[1000], EvenQ[Numerator[DivisorSigma[1, #] / # ]] && OddQ[Denominator[DivisorSigma[1, #]/#]]&] (* _Vincenzo Librandi_, Jun 24 2014 *)
%t nedoQ[n_]:=Module[{ds=DivisorSigma[1,n]/n},EvenQ[Numerator[ds]]&&OddQ[ Denominator[ ds]]]; Select[Range[200],nedoQ] (* _Harvey P. Dale_, Feb 28 2015 *)
%o (PARI) eoab(n) = {for (i=1, n, ab = sigma(i)/i; if ((numerator(ab) % 2 == 0) && (denominator(ab) % 2 == 1), print1(i, ", ")););}
%Y Cf. A216780, A216781, A324903 (characteristic function).
%Y Subsequences: A000396, A027687, A043305 (without its initial 1), A046061, A046388, A065091, A336702 (without its initial 1).
%K nonn,easy
%O 1,1
%A _Michel Marcus_, Sep 16 2012
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