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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.
4
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
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 04 2002
STATUS
approved