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

2, 4, 8, 16, 18, 20, 24, 32, 36, 40, 48, 50, 52, 64, 68, 72, 80, 88, 96, 98, 100, 104, 112, 116, 128, 136, 144, 148, 152, 160, 162, 164, 176, 180, 192, 196, 200, 208, 212, 224, 232, 240, 242, 244, 256, 272, 288, 292, 296, 304, 320, 324, 328, 338, 344, 352

Offset: 1

Author

Michel Marcus, Sep 16 2012

Keywords

• nonn

Comments

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

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

Select[Range[1000], OddQ[Numerator[DivisorSigma[1, #]/#]] && EvenQ[Denominator[DivisorSigma[1, #]/#]] &] (* Vincenzo Librandi, Jun 24 2014 *)

PARI

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