cp's OEIS Frontend

Two consecutive numbers, say n and n+1, cannot share a prime factor (gcd(n, n+1)=1). However, their prime tower factorizations can share some prime numbers; this is the case iff a(n)>1 (see A182318 for the definition of the prime tower factorization of a number).

If p is prime, then a(p-1) = a(p) = 1.

If p is an odd prime, then a(p^2) = 2.

This sequence contains a multiple of p for any prime p:

- let m = A074792(p)^p-1,

- m is a multiple of p, hence p divides A279513(m),

- m+1 = A074792(p)^p, hence p divides A279513(m+1),

- hence p divides gcd(A279513(m), A279513(m+1)) = a(m).

This sequence contains infinitely many distinct values; see A284821 for these distinct values in order of appearance, and A284822 for the corresponding indexes.