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

1,2

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A156345 A078390 A354038 * A279731 A037408 A178680

Adjacent sequences: A216777 A216778 A216779 * A216781 A216782 A216783

Keyword

nonn,easy

Author

Michel Marcus, Sep 16 2012

Status

approved