bibkey: ianakiev2014a008474 authors: Ivan N. Ianakiev; Olivier Gérard year: 2014 title: “OEIS A008474, If n = Product (p_j^k_j) then a(n) = Sum (p_j + k_j)” doi: null url: https://oeis.org/A008474 claim: “A008474 %N: If n = Product (p_j^k_j) then a(n) = Sum (p_j + k_j). A008474 %C: Conjecture: for m > 4, by iterating the map m -> A008474(m) one always reaches 5 [tested up to m = 320000]. - Ivan N. Ianakiev, Nov 10 2014 A008474 %F: Additive with a(p^e) = p + e. A008474 %A: Olivier Gérard” strata_touched:

• D5/S3/Factorization/IanakievPrimeExponentSumIterationReachesFive license: citation-only triage: anchor

OEIS A008474

The entry defines an additive prime-exponent readout by summing each distinct prime divisor of an integer together with its exponent. It asks whether every orbit starting above four reaches five.

Verified locator

• URL: https://oeis.org/A008474
• COMMENTS: Conjecture: for m > 4, by iterating the map m -> A008474(m) one always reaches 5 [tested up to m = 320000]. - Ivan N. Ianakiev, Nov 10 2014

The conjecture is proved for every m > 4; five lies on the cycle 5 -> 6 -> 7 -> 8 -> 5, four is a fixed point so the bound is sharp, and a(1) = 0 follows the entry’s convention.