A216782 Numbers such that numerator(sigma(n)/n) is even and denominator(sigma(n)/n) is odd.

3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 21, 22, 23, 27, 28, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 51, 53, 54, 55, 57, 59, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 75, 77, 78, 79, 83, 84, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 99, 101, 102

Offset

1,1

Comments

a(n) contains odd primes (A065091), odd squarefree semiprimes (A046388), perfect numbers (A000396), and 2n-multiperfect (A027687, A046061).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..8000

Example

sigma(3)/3 = 4/3 (even/odd).

Mathematica

Select[Range[1000], EvenQ[Numerator[DivisorSigma[1, #] / # ]] && OddQ[Denominator[DivisorSigma[1, #]/#]]&] (* Vincenzo Librandi, Jun 24 2014 *)
nedoQ[n_]:=Module[{ds=DivisorSigma[1, n]/n}, EvenQ[Numerator[ds]]&&OddQ[ Denominator[ ds]]]; Select[Range[200], nedoQ] (* Harvey P. Dale, Feb 28 2015 *)

Prog

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

Crossrefs

Cf. A216780, A216781, A324903 (characteristic function).

Subsequences: A000396, A027687, A043305 (without its initial 1), A046061, A046388, A065091, A336702 (without its initial 1).

Sequence in context: A046839 A003601 A328557 * A328952 A072600 A047582

Adjacent sequences: A216779 A216780 A216781 * A216783 A216784 A216785

Keyword

nonn,easy

Author

Michel Marcus, Sep 16 2012

Status

approved