A324719 - OEIS

%I #21 Mar 11 2024 08:50:12

%S 3,7,15,27,31,51,55,63,111,119,123,125,127,219,255,411,447,485,493,

%T 495,505,511,735,765,771,831,879,927,959,965,985,1011,1023,1563,1587,

%U 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

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

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

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

%C 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.

%H Antti Karttunen, <a href="/A324719/b324719.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

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

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

%K nonn,look

%O 1,1

%A _Antti Karttunen_, Mar 14 2019