A216780 - OEIS

%I #24 Jun 24 2014 03:19:05

%S 1,9,10,12,25,26,34,44,49,56,58,74,76,81,82,90,106,120,121,122,146,

%T 169,172,178,184,194,202,216,218,225,226,234,236,260,268,274,289,298,

%U 300,306,312,314,332,340,346,361,362,386,394,396,408,428,440,441,458

%N Numbers n such that numerator(sigma(n)/n) and denominator(sigma(n)/n) are both odd.

%C a(n) contains odd squares (A016754), 3-perfect numbers (A005820) and 5-perfect numbers (A046060).

%C This is also the sequence of numbers x such that A243473(x) is even. - _Michel Marcus_, Jun 06 2014

%H Vincenzo Librandi, <a href="/A216780/b216780.txt">Table of n, a(n) for n = 1..1000</a>

%e sigma(10)/10 = 9/5; both 9 and 5 are odd, so 10 is in the sequence.

%t Select[Range[500], OddQ[Numerator[DivisorSigma[1, #]/#]] && OddQ[Denominator[DivisorSigma[1, #]/#]] &] (* _Alonso del Arte_, Sep 16 2012 *)

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

%Y Cf. A216781, A216782, A016754, A005820, A046060.

%K nonn,easy

%O 1,2

%A _Michel Marcus_, Sep 16 2012