bibkey: wiseman2019a258409 authors: Gus Wiseman year: 2019 title: “OEIS A258409, Greatest common divisor of all (d-1)’s, where the d’s are the positive divisors of n” doi: null url: https://oeis.org/A258409 claim: “Greatest common divisor of all (d-1)’s, where the d’s are the positive divisors of n. Conjecture: a(n) = A289508(A328023(n)) = GCD of the differences between consecutive divisors of n. See A328163 and A328164. - Gus Wiseman, Oct 16 2019. Heinz number of the multiset of differences between consecutive divisors of n. The Heinz number of an integer partition or multiset {y_1,…,y_k} is prime(y_1)*…*prime(y_k). a(n) is the GCD of the indices j for which the j-th prime p_j divides n.” strata_touched:

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

OEIS A258409

OEIS A258409 defines the sequence by the following name:

Greatest common divisor of all (d-1)’s, where the d’s are the positive divisors of n.

Its comment by Gus Wiseman on October 16, 2019 gives the three-term conjecture quoted below. The two auxiliary entries define the intervening transforms:

Heinz number of the multiset of differences between consecutive divisors of n.

The Heinz number of an integer partition or multiset {y_1,…,y_k} is prime(y_1)*…*prime(y_k).

a(n) is the GCD of the indices j for which the j-th prime p_j divides n.

The prime indices in these descriptions are one-based: the first prime is 2.

Verified locator

• URL: https://oeis.org/A258409
• Locator: COMMENTS, Gus Wiseman, Oct 16 2019.

Conjecture: a(n) = A289508(A328023(n)) = GCD of the differences between consecutive divisors of n. See A328163 and A328164. - Gus Wiseman, Oct 16 2019