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A324897
Odd numbers k such that A318458(k) (bitwise-AND of k and sigma(k)-k) is equal to k.
4
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 19 2019
STATUS
approved