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A216780 Numbers n such that numerator(sigma(n)/n) and denominator(sigma(n)/n) are both odd. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A078459 A156345 A078390 * A279731 A037408 A178680

Adjacent sequences:  A216777 A216778 A216779 * A216781 A216782 A216783

KEYWORD

nonn,easy

AUTHOR

Michel Marcus, Sep 16 2012

STATUS

approved

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Last modified June 20 08:57 EDT 2021. Contains 345162 sequences. (Running on oeis4.)