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A359084
Numbers k such that A246601(k) > 2*k.
2
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
1,1
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).
MATHEMATICA
s[n_] := DivisorSum[n, # &, BitAnd[n, #] == # &]; Select[Range[10^6], s[#] > 2*# &]
PROG
(PARI) is(n) = sumdiv(n, d, d * (bitor(n, d) == n)) > 2*n;
CROSSREFS
Cf. A000203 (sigma), A000396, A103292, A246601.
Subsequence of A005101.
A359085 is a subsequence.
Sequence in context: A145591 A103289 A038463 * A043452 A261593 A290869
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Dec 15 2022
STATUS
approved