A043305 - OEIS

%I #30 Mar 21 2023 09:22:52

%S 1,3,6,7,15,21,28,31,33,42,69,84,91,93,105,127,135,141,186,217,231,

%T 270,273,285,381,420,465,483,496,546,573,651,762,775,819,861,868,889,

%U 924,945,987,1023,1149,1185,1302,1365,1419,1485,1488,1561,1638,1743,1890

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

%C 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

%H Amiram Eldar, <a href="/A043305/b043305.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..910 from Harvey P. Dale)

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

%o (PARI) isok(n) = (ispower(num = numerator(sigma(n)/n), , &s) && (s == 2)) || (num == 2) || (num == 1); \\ _Michel Marcus_, Nov 21 2013

%o (PARI) isA043305(n) = { n=sigma(n)/gcd(sigma(n),n); !bitand(n,n-1); }; \\ _Antti Karttunen_, Mar 20 2023

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

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

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Apr 04 2002