A359084 Numbers k such that A246601(k) > 2*k.

4095, 8190, 16380, 32760, 65520, 131040, 262080, 524160, 1048320, 2096640, 4193280, 8386560, 16773120, 16777215, 33546240, 33550335, 33554430, 67092480, 67096575, 67100670, 67108860, 134184960, 134189055, 134193150, 134201340, 134217720, 268369920, 268374015

Offset: 1

Author

Amiram Eldar, Dec 15 2022

Keywords

• nonn
• base

Comments

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.

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).

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

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).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..208
• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to divisors of numbers.

Crossrefs

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

Subsequence of A005101.

A359085 is a subsequence.

Programs

Mathematica

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

PARI

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