This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A359084 #12 Dec 26 2022 09:45:30 %S A359084 4095,8190,16380,32760,65520,131040,262080,524160,1048320,2096640, %T A359084 4193280,8386560,16773120,16777215,33546240,33550335,33554430, %U A359084 67092480,67096575,67100670,67108860,134184960,134189055,134193150,134201340,134217720,268369920,268374015 %N A359084 Numbers k such that A246601(k) > 2*k. %C A359084 An analog of abundant numbers k (A005101), in which the divisor sum is restricted to divisors d whose 1-bits in their binary expansions are common with those of k. %C A359084 If k is a term then 2*k is also a term. Therefore all the terms can be generated from the primitive set of the odd terms (A359085). %C A359084 The least term that is not divisible by 4095 is a(208) = 1099511627775 = 2^40 - 1. %C A359084 Since A246601(2^k-1) = sigma(2^k-1), 2^k-1 is a term for all k in A103292, unless 2^k-1 is an odd perfect number (A000396). %H A359084 Amiram Eldar, <a href="/A359084/b359084.txt">Table of n, a(n) for n = 1..208</a> %H A359084 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>. %H A359084 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>. %t A359084 s[n_] := DivisorSum[n, # &, BitAnd[n, #] == # &]; Select[Range[10^6], s[#] > 2*# &] %o A359084 (PARI) is(n) = sumdiv(n, d, d * (bitor(n, d) == n)) > 2*n; %Y A359084 Cf. A000203 (sigma), A000396, A103292, A246601. %Y A359084 Subsequence of A005101. %Y A359084 A359085 is a subsequence. %K A359084 nonn,base %O A359084 1,1 %A A359084 _Amiram Eldar_, Dec 15 2022