bibkey: krizek2014a245786 authors: Jaroslav Krizek year: 2014 title: “OEIS A245786, Numbers n such that k(n) = (n/tau(n) + sigma(n)/n) is an integer” doi: null url: https://oeis.org/A245786 claim: “Numbers n such that k(n) = (n/tau(n) + sigma(n)/n) is an integer. Conjecture: Subsequence of A216793. Numbers n such that gcd(sigma(n), n) > gcd(sigma(m), m) for all m < n. - Michel Marcus, Sep 16 2012 Jaroslav Krizek, Aug 15 2014” strata_touched:

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

OEIS A245786

The NAME of A245786 states:

Numbers n such that k(n) = (n/tau(n) + sigma(n)/n) is an integer.

The conjecture is printed as:

Conjecture: Subsequence of A216793.

OEIS A216793 states:

Numbers n such that gcd(sigma(n), n) > gcd(sigma(m), m) for all m < n.

The A216793 entry attributes that NAME to Michel Marcus, Sep 16 2012. The A245786 author line is:

Jaroslav Krizek, Aug 15 2014

The certified values at 275890944 and 142990848 refute only the literal subsequence conjecture. No corrected statement or exhaustive literature claim follows.

Verified locator

• URL: https://oeis.org/A245786
• NAME (verbatim): Numbers n such that k(n) = (n/tau(n) + sigma(n)/n) is an integer.
• COMMENTS conjecture line (verbatim): Conjecture: Subsequence of A216793.
• A216793 NAME (verbatim): Numbers n such that gcd(sigma(n), n) > gcd(sigma(m), m) for all m < n.
• A216793 attribution: Michel Marcus, Sep 16 2012
• AUTHOR (verbatim): Jaroslav Krizek, Aug 15 2014