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

Author

Benoit Cloitre, Apr 04 2002

Keywords

• easy
• nonn

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)

Crossrefs

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

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

Programs

Mathematica

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

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