%I #12 Dec 26 2022 09:45:30

%S 4095,8190,16380,32760,65520,131040,262080,524160,1048320,2096640,

%T 4193280,8386560,16773120,16777215,33546240,33550335,33554430,

%U 67092480,67096575,67100670,67108860,134184960,134189055,134193150,134201340,134217720,268369920,268374015

%N Numbers k such that A246601(k) > 2*k.

%C 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 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 The least term that is not divisible by 4095 is a(208) = 1099511627775 = 2^40 - 1.

%C 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 Amiram Eldar, <a href="/A359084/b359084.txt">Table of n, a(n) for n = 1..208</a>

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

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>.

%t s[n_] := DivisorSum[n, # &, BitAnd[n, #] == # &]; Select[Range[10^6], s[#] > 2*# &]

%o (PARI) is(n) = sumdiv(n, d, d * (bitor(n, d) == n)) > 2*n;

%Y Cf. A000203 (sigma), A000396, A103292, A246601.

%Y Subsequence of A005101.

%Y A359085 is a subsequence.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Dec 15 2022