cp's OEIS Frontend

A324897 Odd numbers k such that A318458(k) (bitwise-AND of k and sigma(k)-k) is equal to k.

%I A324897 #21 Jul 18 2021 07:13:12
%S A324897 7425,76545,92565,236925,831105,954765,1401345,2011905,2048445,
%T A324897 2129985,2253825,2445345,2621745,2974725,3283245,3847725,5709825,
%U A324897 6447105,8422785,8503425,8945685,10781505,12488385,13470345,14322945,15213825,15340545,19470465,19502145,20075265,22749825,25740225,25756605,26215245,27009045
%N A324897 Odd numbers k such that A318458(k) (bitwise-AND of k and sigma(k)-k) is equal to k.
%C A324897 If this sequence has no common terms with A324647, or no terms common with A324727, then there are no odd perfect numbers.
%C A324897 The first 16 terms factored:
%C A324897       7425 = 3^3 * 5^2 * 11,
%C A324897      76545 = 3^7 * 5 * 7,
%C A324897      92565 = 3^2 * 5 * 11^2 * 17,
%C A324897     236925 = 3^6 * 5^2 * 13,
%C A324897     831105 = 3^2 * 5 * 11 * 23 * 73,
%C A324897     954765 = 3^2 * 5 * 7^2 * 433,
%C A324897    1401345 = 3^2 * 5 * 11 * 19 * 149,
%C A324897    2011905 = 3^3 * 5 * 7 * 2129,
%C A324897    2048445 = 3^2 * 5 * 7^2 * 929,
%C A324897    2129985 = 3^2 * 5 * 11 * 13 * 331,
%C A324897    2253825 = 3^5 * 5^2 * 7 * 53,
%C A324897    2445345 = 3^2 * 5 * 7^2 * 1109,
%C A324897    2621745 = 3^2 * 5 * 7^2 * 29 * 41,
%C A324897    2974725 = 3^4 * 5^2 * 13 * 113,
%C A324897    3283245 = 3^2 * 5 * 7^2 * 1489,
%C A324897    3847725 = 3^2 * 5^2 * 7^2 * 349.
%H A324897 Antti Karttunen, <a href="/A324897/b324897.txt">Table of n, a(n) for n = 1..611</a>
%H A324897 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324897 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%H A324897 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A324897 Select[Range[1, 10^7, 2], BitAnd[#, DivisorSigma[1, #] - #] == # &] (* _Michael De Vlieger_, Jun 22 2019, after _Vincenzo Librandi_ at A318458 *)
%o A324897 (PARI) isok(k) = (k%2) && (bitand(k, sigma(k)-k) == k); \\ _Michel Marcus_, Jul 18 2021
%Y A324897 Subsequence of A324649.
%Y A324897 Cf. A318458, A324647, A324898 (a subsequence).
%K A324897 nonn
%O A324897 1,1
%A A324897 _Antti Karttunen_, Apr 19 2019