A216780 Numbers n such that numerator(sigma(n)/n) and denominator(sigma(n)/n) are both odd.

1, 9, 10, 12, 25, 26, 34, 44, 49, 56, 58, 74, 76, 81, 82, 90, 106, 120, 121, 122, 146, 169, 172, 178, 184, 194, 202, 216, 218, 225, 226, 234, 236, 260, 268, 274, 289, 298, 300, 306, 312, 314, 332, 340, 346, 361, 362, 386, 394, 396, 408, 428, 440, 441, 458

Offset: 1

Author

Michel Marcus, Sep 16 2012

Keywords

• nonn
• easy

Comments

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

This is also the sequence of numbers x such that A243473(x) is even. - Michel Marcus, Jun 06 2014

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

Select[Range[500], OddQ[Numerator[DivisorSigma[1, #]/#]] && OddQ[Denominator[DivisorSigma[1, #]/#]] &] (* Alonso del Arte, Sep 16 2012 *)

PARI

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