bibkey: wilson2015a260310
authors: Robert G. Wilson v; Juri-Stepan Gerasimov
year: 2015
title: "OEIS A260310, Pairs with balanced sums of prime divisors (A008472) and inverse prime divisors (A069359), ordered by larger members"
doi: null
url: https://oeis.org/A260310
claim: "Pairs with balanced sums of prime divisors (A008472) and inverse prime divisors (A069359), ordered by larger members. Consider pairs (x,y) of numbers where sum(p|x) p + sum(q|y) q = x*sum(p|x) 1/p + y*sum(q|y) 1/q where p, q are primes and sum(p|x) p > sum(q|y) q. Conjecture: if a(2n-1) is prime then a(2n) is composite and vice versa. And when a(2n-1) is composite, it is congruent to 0 (mod 6). - _Robert G. Wilson v_, Jul 22 2015 _Juri-Stepan Gerasimov_, Jul 22 2015"
strata_touched:
  - D5/S3/Arith/Congruence/WilsonBalancedPrimeDivisorPairModSixRefutation
license: citation-only
triage: anchor

OEIS A260310

The NAME of A260310 states:

Pairs with balanced sums of prime divisors (A008472) and inverse prime divisors (A069359), ordered by larger members.

The COMMENTS definition is printed as:

Consider pairs (x,y) of numbers where sum(p|x) p + sum(q|y) q = xsum(p|x) 1/p + ysum(q|y) 1/q where p, q are primes and sum(p|x) p > sum(q|y) q.

The COMMENTS conjecture is printed as:

Conjecture: if a(2n-1) is prime then a(2n) is composite and vice versa. And when a(2n-1) is composite, it is congruent to 0 (mod 6). - Robert G. Wilson v, Jul 22 2015

The AUTHOR line is:

Juri-Stepan Gerasimov, Jul 22 2015

Only the mod-six clause is refuted, by the balanced pair (140140, 141601) outside the published b-file range. Minimality is not claimed.

Verified locator

• URL: https://oeis.org/A260310
• NAME (verbatim): Pairs with balanced sums of prime divisors (A008472) and inverse prime divisors (A069359), ordered by larger members.
• COMMENTS definition line (verbatim): Consider pairs (x,y) of numbers where sum(p|x) p + sum(q|y) q = xsum(p|x) 1/p + ysum(q|y) 1/q where p, q are primes and sum(p|x) p > sum(q|y) q.
• COMMENTS conjecture line (verbatim): Conjecture: if a(2n-1) is prime then a(2n) is composite and vice versa. And when a(2n-1) is composite, it is congruent to 0 (mod 6). - Robert G. Wilson v, Jul 22 2015
• AUTHOR (verbatim): Juri-Stepan Gerasimov, Jul 22 2015