bibkey: krizek2017a280258 authors: Jaroslav Krizek year: 2017 title: “OEIS A280258, sum of phitorials over divisors” doi: null url: https://oeis.org/A280258 claim: “A280258 %N: a(n) = Sum_{d|n} pxi(d), where pxi(m) is the product of totatives of m (A001783). A280258 %C: Conjecture: a(n) is odd for numbers in A183300; a(n) is even for numbers in A001105 (2*n^2). A280258 %A: Jaroslav Krizek, Jan 01 2017” strata_touched:

• D5/S3/Arith/KrizekPhitorialDivisorSumParity license: citation-only triage: anchor

OEIS A280258

The NAME line defines a(n) as the sum of pxi(d) over the positive divisors d of n, where A001783 defines pxi(m) as the product of the integers from one through m that are relatively prime to m.

The COMMENT conjectures that a(n) is odd on A183300, the positive integers not of the form 2*k^2, and even on A001105, the integers of the form 2*k^2.

Verified locator

• URL: https://oeis.org/A280258
• NAME (verbatim): a(n) = Sum_{d|n} pxi(d), where pxi(m) is the product of totatives of m (A001783).
• COMMENT (verbatim): Conjecture: a(n) is odd for numbers in A183300; a(n) is even for numbers in A001105 (2*n^2).
• AUTHOR (verbatim): Jaroslav Krizek, Jan 01 2017