Metadata
bibkey: lagneau2012a193351
authors: Michel Lagneau
year: 2012
title: "OEIS A193351, Numbers k such that A071324(k) is prime"
doi: null
url: https://oeis.org/A193351
claim: "A193351 %N: Numbers k such that A071324(k) is prime. A193351 %C: Numbers k such that the alternating sum of all divisors of k (divisors nonincreasing, starting with k) is prime. A193351 %C: For k > 3, if the alternating sum of all divisors of k (divisors nonincreasing, starting with k) is a prime number, then k is either a square or twice a square. A193351 %C: This conjecture is verified up to k <= 10^8. - _Shreyansh Jaiswal_, Apr 25 2025 A193351 %A: _Michel Lagneau_, Dec 20 2012"
strata_touched:
- D5/S3/Arith/LagneauAlternatingDivisorSumPrimeSquare
license: citation-only
triage: anchor
OEIS A193351
The entry selects the natural numbers whose A071324 value, the alternating sum of their divisors in nonincreasing order, is prime.
The entry records Lagneau’s conjecture that every selected number greater than three is a square or twice a square.
Verified locator
- URL: https://oeis.org/A193351
- Locator: COMMENTS, “For k > 3, if the alternating sum of all divisors of k (divisors nonincreasing, starting with k) is a prime number, then k is either a square or twice a square.”
The mathematical core is the classical parity fact that sigma(n) is odd if and only if n is a square or twice a square; no priority claim is made.