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A324897 Odd numbers n such that A318458(n) (bitwise-AND of n and sigma(n)-n) is equal to n. 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 (list; graph; refs; listen; history; text; internal format)
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 *)

CROSSREFS

Subsequence of A324649.

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

Sequence in context: A023940 A116195 A249878 * A051259 A289517 A178281

Adjacent sequences:  A324894 A324895 A324896 * A324898 A324899 A324900

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 19 2019

STATUS

approved

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Last modified July 2 02:41 EDT 2020. Contains 335389 sequences. (Running on oeis4.)