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

1,1

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)

Mathematica

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

Prog

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

Crossrefs

Subsequence of A324649.

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

Sequence in context: A249878 A360328 A360355 * A051259 A289517 A178281

Adjacent sequences: A324894 A324895 A324896 * A324898 A324899 A324900

Keyword

nonn

Author

Antti Karttunen, Apr 19 2019

Status

approved