Metadata
bibkey: gerasimov2015a254748
authors: Juri-Stepan Gerasimov
year: 2015
title: "OEIS A254748, Numbers without superdivisors"
doi: null
url: https://oeis.org/A254748
claim: "A254748 %N: Numbers without superdivisors: numbers n such that n/k + n fails to divide at least one of (n/k)^(n/k) + n, (n/k)^n + n/k or n^(n/k) + n/k for any divisor k of n. A254748 %C: Zerosuperdivisor numbers. Numbers n such that A247477(n) = 0. A254748 %C: Conjecture: Average of twin prime pairs (A014574) are zerosuperdivisor numbers. A254748 %A: _Juri-Stepan Gerasimov_, Feb 07 2015"
strata_touched:
- D5/S3/Arith/Congruence/GerasimovTwinPrimeMeanNoSuperdivisor
license: citation-only
triage: anchor
OEIS A254748
The entry defines numbers without superdivisors by the three divisibility tests in A247477. It states that averages of twin prime pairs are zerosuperdivisor numbers.
The proof of the twin-prime mean claim is an elementary multiplicative-order argument; no priority claim is made.
Verified locator
- URL: https://oeis.org/A254748
- Locator: COMMENTS, “Conjecture: Average of twin prime pairs (A014574) are zerosuperdivisor numbers.”
Charlie Neder’s 2019 A247477 comment gives the known partial odd-d characterization of superdivisors. The proof here is an elementary multiplicative-order argument, with no priority claim.