A043305 Numbers k such that the numerator of the sum of the reciprocals of the divisors of k (=A017665(k)) is a power of 2.

1, 3, 6, 7, 15, 21, 28, 31, 33, 42, 69, 84, 91, 93, 105, 127, 135, 141, 186, 217, 231, 270, 273, 285, 381, 420, 465, 483, 496, 546, 573, 651, 762, 775, 819, 861, 868, 889, 924, 945, 987, 1023, 1149, 1185, 1302, 1365, 1419, 1485, 1488, 1561, 1638, 1743, 1890

Offset

1,2

Comments

After 1, a subsequence of A216782. If both x and y are terms and gcd(x, y) = 1, then x*y is also present. - Antti Karttunen, Mar 20 2023

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..910 from Harvey P. Dale)

Mathematica

Select[Range[2000], IntegerQ[Log[2, Numerator[Total[1/Divisors[#]]]]]&] (* Harvey P. Dale, Nov 29 2014 *)

Prog

(PARI) isok(n) = (ispower(num = numerator(sigma(n)/n), , &s) && (s == 2)) || (num == 2) || (num == 1); \\ Michel Marcus, Nov 21 2013
(PARI) isA043305(n) = { n=sigma(n)/gcd(sigma(n), n); !bitand(n, n-1); }; \\ Antti Karttunen, Mar 20 2023

Crossrefs

Cf. A017665, A216782, A361465 (characteristic function).

Subsequences: A000396, A336702, A348943 (odd terms).

Sequence in context: A124611 A281900 A266615 * A227723 A192124 A334210

Adjacent sequences: A043302 A043303 A043304 * A043306 A043307 A043308

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 04 2002

Status

approved