A324719 Odd numbers n for which bitor(2n,sigma(n)) = 2*bitor(n,sigma(n)-n), where bitor is bitwise-OR, A003986.

3, 7, 15, 27, 31, 51, 55, 63, 111, 119, 123, 125, 127, 219, 255, 411, 447, 485, 493, 495, 505, 511, 735, 765, 771, 831, 879, 927, 959, 965, 985, 1011, 1023, 1563, 1587, 1611, 1731, 1779, 1791, 1799, 1887, 1921, 1923, 1945, 1975, 1983, 1991, 2019, 2031, 2041, 2043, 2045, 2047, 3099, 3183, 3231, 3279, 3291, 3327, 3459, 3535, 3579

Offset: 1

Author

Antti Karttunen, Mar 14 2019

Keywords

• nonn
• look

Comments

Odd numbers n for which 2*A318456(n) = A318466(n).

If there are no common terms with A324718, then there are no odd perfect numbers.

The following subsequence of terms k are those with sigma(k) == 2 (mod 4): 3725, 7281, 15325, 24525, 25713, 32481, 51633, 52209, 59121, 63553, 114417, 117009, 120753, 121725, 122725, 123245, 130833, 208881, 236925, 241325, 245725, 253325, 261297, 384993, 411633, 457713, 468081, 482481, 482525, 482725, 483325, ..., and are thus present in A191218.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• 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

Cf. A003986, A191218, A318456, A318466, A324718, A324727.

Programs

Mathematica

Select[Range[1, 10^4, 2], Block[{s = DivisorSigma[1, #]}, BitOr[2*#, s] == 2* BitOr[#, s-#]] &] (* Paolo Xausa, Mar 11 2024 *)

PARI

for(n=1,oo,if((n%2) && (2*(bitor(n, sigma(n)-n))==bitor(n+n, sigma(n))),print1(n,", ")));