bibkey: krizek2018a300657 authors: Jaroslav Krizek year: 2018 title: “OEIS A300657, sum of divisor-sum residues” doi: null url: https://oeis.org/A300657 claim: “%N a(n) = Sum_{d|n} sigma(d) mod d. %C Conjecture: a(n) = A054024(n) only for the noncomposite numbers A008578.” strata_touched:

• D5/S3/ArithSums/KrizekDivisorSigmaModNoncomposite license: citation-only triage: anchor

OEIS A300657

The entry defines a(n) as the sum, over the positive divisors d of n, of sigma(d) mod d. Its unsigned Comment line conjectures that a(n) = A054024(n) exactly for the noncomposite numbers A008578, where A054024(n) = sigma(n) mod n and A008578 consists of one and the primes. By OEIS convention the unsigned line is attributed to the entry author, Jaroslav Krizek.

The entry also records Robert Israel’s formulas for products of two distinct primes and for prime powers. Those families do not include all composites; for example, 60 = 2^2 * 3 * 5 belongs to neither family.

Verified locator

• URL: https://oeis.org/A300657
• %N (verbatim): a(n) = Sum_{d|n} sigma(d) mod d.
• %C (verbatim): a(n) >= A054024(n). Conjecture: a(n) = A054024(n) only for the noncomposite numbers A008578.
• %A (verbatim): Jaroslav Krizek, Mar 10 2018