cp's OEIS Frontend

A324643 Numbers k such that bitand(2k,sigma(k))/2 = k = bitand(k,sigma(k)-k), where bitand is bitwise-AND, A004198.

%I A324643 #36 Jan 08 2025 17:02:06
%S A324643 6,20,28,36,88,100,104,264,272,304,368,392,464,496,550,784,1032,1040,
%T A324643 1044,1056,1068,1104,1120,1184,1232,1312,1376,1504,1696,1888,1952,
%U A324643 2140,3222,4100,4128,4160,4288,4512,4544,4624,4640,4672,5056,5312,5696,6208,6328,6464,6592,6808,6848,6976,7232,7304,8128,8288,8968,9256,10184
%N A324643 Numbers k such that bitand(2k,sigma(k))/2 = k = bitand(k,sigma(k)-k), where bitand is bitwise-AND, A004198.
%C A324643 Numbers k for which k = A318458(k)/2 = A318468(k).
%C A324643 Intersection of A324649 and A324652.
%C A324643 It is conjectured that there are no odd terms in this sequence, which is equivalent to the conjecture that there are no odd perfect numbers.
%C A324643 Question: Where do the densest clusters of terms occur? See also the scatter plot. - _Antti Karttunen_, Mar 12 2024
%C A324643 As A324649 and A324652 are both subsequences of nondeficient numbers (A023196), also this sequence is, which stems from the "monotonic property" of bitwise-and. - _Antti Karttunen_, Jan 08 2025
%H A324643 Antti Karttunen, <a href="/A324643/b324643.txt">Table of n, a(n) for n = 1..17020</a>
%H A324643 Michael De Vlieger, <a href="/A324643/a324643.png">Log log scatterplot of a(n)</a>, n = 1..17020, labeling cusps in the plot.
%H A324643 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324643 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%H A324643 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A324643 Select[Range[10^4], Block[{s = DivisorSigma[1, #]}, # == BitAnd[#, s-#] && 2*# == BitAnd[2*#, s]] &] (* _Paolo Xausa_, Mar 11 2024 *)
%o A324643 (PARI) for(n=1,oo,if( (bitand(n, sigma(n)-n)==n) && (bitand(n+n, sigma(n))==2*n),print1(n,", ")))
%Y A324643 Cf. A004198, A318458, A318468.
%Y A324643 Intersection of A324649 and A324652.
%Y A324643 Subsequence of A023196 and of A324639.
%K A324643 nonn,look
%O A324643 1,1
%A A324643 _Antti Karttunen_, Mar 14 2019