A361128 -id:A361128 - cp's OEIS frontend

A361129 Let b = A360519; let Lg = gcd(b(n-1),b(n)), Rg = gcd(b(n),b(n+1)); let L(n) = prod_{primes p|Lg} p-part of b(n), R(n) = prod_{primes p|Rg} p-part of b(n), M(n) = b(n)/(L(n)*R(n)); sequence gives M(n).

3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 11, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 5, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1

Offset: 2

Scott R. Shannon, Rémy Sigrist, and N. J. A. Sloane, Mar 09 2023

nonn

The p-part of a number k is the highest power of p that divides k. For example, the 2-part of 24 is 8, the 3-part is 3.
Since so many of the initial terms are 1, we show more than the usual number of terms in the DATA section.
Conjecture: All terms are odd, and every odd number eventually appears.

N. J. A. Sloane, Table of n, a(n) for n = 2..20000

Cf. A360519, A361118, A361128, A361130.

A361130 Let b = A360519; let Lg = gcd(b(n-1),b(n)), Rg = gcd(b(n),b(n+1)); let L(n) = prod_{primes p|Lg} p-part of b(n), R(n) = prod_{primes p|Rg} p-part of b(n), M(n) = b(n)/(L(n)*R(n)); sequence gives R(n).

Original entry on oeis.org

2, 5, 7, 3, 4, 5, 11, 3, 2, 7, 11, 9, 5, 8, 11, 13, 3, 8, 7, 13, 5, 2, 17, 7, 9, 4, 13, 17, 3, 2, 19, 5, 9, 16, 11, 17, 5, 2, 23, 3, 19, 4, 13, 9, 25, 2, 29, 3, 31, 2, 7, 3, 37, 2, 17, 9, 41, 2, 5, 23, 7, 12, 5, 29, 7, 2, 27, 43, 5, 4, 3, 47, 5, 2, 9, 49, 19, 8, 3, 5, 31, 4, 43, 7

Offset: 2