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

7425, 76545, 92565, 236925, 831105, 954765, 1401345, 2011905, 2048445, 2129985, 2253825, 2445345, 2621745, 2974725, 3283245, 3847725, 5709825, 6447105, 8422785, 8503425, 8945685, 10781505, 12488385, 13470345, 14322945, 15213825, 15340545, 19470465, 19502145, 20075265, 22749825, 25740225, 25756605, 26215245, 27009045

Offset: 1

Author

Antti Karttunen, Apr 19 2019

Keywords

• nonn

Comments

If this sequence has no common terms with A324647, or no terms common with A324727, then there are no odd perfect numbers.

The first 16 terms factored:

7425 = 3^3 * 5^2 * 11,

76545 = 3^7 * 5 * 7,

92565 = 3^2 * 5 * 11^2 * 17,

236925 = 3^6 * 5^2 * 13,

831105 = 3^2 * 5 * 11 * 23 * 73,

954765 = 3^2 * 5 * 7^2 * 433,

1401345 = 3^2 * 5 * 11 * 19 * 149,

2011905 = 3^3 * 5 * 7 * 2129,

2048445 = 3^2 * 5 * 7^2 * 929,

2129985 = 3^2 * 5 * 11 * 13 * 331,

2253825 = 3^5 * 5^2 * 7 * 53,

2445345 = 3^2 * 5 * 7^2 * 1109,

2621745 = 3^2 * 5 * 7^2 * 29 * 41,

2974725 = 3^4 * 5^2 * 13 * 113,

3283245 = 3^2 * 5 * 7^2 * 1489,

3847725 = 3^2 * 5^2 * 7^2 * 349.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..611
• Index entries for sequences related to binary expansion of n
• Index entries for sequences where any odd perfect numbers must occur
• Index entries for sequences related to sigma(n)

Crossrefs

Subsequence of A324649.

Cf. A318458, A324647, A324898 (a subsequence).

Programs

Mathematica

Select[Range[1, 10^7, 2], BitAnd[#, DivisorSigma[1, #] - #] == # &] (* Michael De Vlieger, Jun 22 2019, after Vincenzo Librandi at A318458 *)

PARI

isok(k) = (k%2) && (bitand(k, sigma(k)-k) == k); \\ Michel Marcus, Jul 18 2021