A338669 The prime tower factorization of a(n) is obtained by replacing the rightmost prime number by 1 in the prime tower factorization of n; a(1) = 1.

1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 8, 5, 2, 3, 4, 1, 6, 1, 2, 3, 2, 5, 12, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 7, 10, 3, 4, 1, 6, 5, 8, 3, 2, 1, 12, 1, 2, 9, 4, 5, 6, 1, 4, 3, 10, 1, 24, 1, 2, 15, 4, 7, 6, 1, 16, 9, 2, 1, 12

Offset: 1

Author

Rémy Sigrist, Apr 23 2021

Keywords

• nonn

Comments

The prime tower factorization of a number is defined in A182318.

Sequence A338668 gives the rightmost prime number.

Examples

			See Links section.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Illustration of initial terms

Crossrefs

Cf. A106490, A182318, A338668.

Programs

PARI

a(n) = { if (n==1, 1, my (f=factor(n), w=#f~, p=f[w,1], e=f[w,2]); if (e==1, n/p, n*p^(a(e)-e))) }

Formula

a(n) = 1 iff n = 1 or n is a prime number.

A106490(a(n)) = 1 + A106490(n) for any n > 1.

a^k(n) = 1 for k = A106490(n) (where a^k denotes the k-th iterate of a).