bibkey: krizek2013a231548 authors: Jaroslav Krizek year: 2013 title: “OEIS A231548, Numbers n such that 2n - 1 < sigma(n) - sigma(n-2)” doi: null url: https://oeis.org/A231548 claim: “Numbers n such that 2n - 1 < sigma(n) - sigma(n-2). Also numbers n such that antisigma(n) < antisigma(n-2), where antisigma(n) = A024816(n) = the sum of the non-divisors of n that are between 1 and n. Conjecture: there are no numbers n such that antisigma(n) < antisigma(n-3). - Jaroslav Krizek, Nov 12 2013 Antisigma(n): Sum of the numbers less than n that do not divide n.” strata_touched:

• D5/S0/Certificates/KrizekAntisigmaDecreaseRefutation license: citation-only triage: anchor

OEIS A231548

The NAME of A231548 states:

Numbers n such that 2*n - 1 < sigma(n) - sigma(n-2).

The COMMENTS define the equivalent antisigma condition:

Also numbers n such that antisigma(n) < antisigma(n-2), where antisigma(n) = A024816(n) = the sum of the non-divisors of n that are between 1 and n.

The conjecture is printed as:

Conjecture: there are no numbers n such that antisigma(n) < antisigma(n-3). - Jaroslav Krizek, Nov 12 2013

OEIS A024816 defines the function by its NAME:

Antisigma(n): Sum of the numbers less than n that do not divide n.

The certified values at 332640 and 332637 refute only the literal universal conjecture. No corrected statement or exhaustive literature claim follows.

Verified locator

• URL: https://oeis.org/A231548
• NAME (verbatim): Numbers n such that 2*n - 1 < sigma(n) - sigma(n-2).
• COMMENTS definition (verbatim): Also numbers n such that antisigma(n) < antisigma(n-2), where antisigma(n) = A024816(n) = the sum of the non-divisors of n that are between 1 and n.
• COMMENTS conjecture line (verbatim): Conjecture: there are no numbers n such that antisigma(n) < antisigma(n-3). - Jaroslav Krizek, Nov 12 2013
• A024816 NAME (verbatim): Antisigma(n): Sum of the numbers less than n that do not divide n.