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A216781 Numbers such that numerator(sigma(n)/n) is odd and denominator(sigma(n)/n) is even. 3

%I

%S 2,4,8,16,18,20,24,32,36,40,48,50,52,64,68,72,80,88,96,98,100,104,112,

%T 116,128,136,144,148,152,160,162,164,176,180,192,196,200,208,212,224,

%U 232,240,242,244,256,272,288,292,296,304,320,324,328,338,344,352

%N Numbers such that numerator(sigma(n)/n) is odd and denominator(sigma(n)/n) is even.

%C a(n) contains powers of 2 (A000079 except 1), and hemiperfect numbers (A055153, A141645, A159271, A160678).

%H Vincenzo Librandi, <a href="/A216781/b216781.txt">Table of n, a(n) for n = 1..1000</a>

%e sigma(2)/2 = 3/2 (odd/even).

%t Select[Range[1000], OddQ[Numerator[DivisorSigma[1, #]/#]] && EvenQ[Denominator[DivisorSigma[1, #]/#]] &] (* _Vincenzo Librandi_, Jun 24 2014 *)

%o (PARI) oeab(n) = {for (i=1, n, ab = sigma(i)/i; if ((numerator(ab) % 2 == 1) && (denominator(ab) % 2 == 0), print1(i, ", ")););}

%Y Cf. A216780, A216782, A000079, A055153, A141645, A159271, A160678.

%K nonn

%O 1,1

%A _Michel Marcus_, Sep 16 2012

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Last modified June 21 01:12 EDT 2021. Contains 345339 sequences. (Running on oeis4.)