A338668 a(n) is the rightmost prime number in prime tower factorization of n; a(1) = 1.

1, 2, 3, 2, 5, 3, 7, 3, 2, 5, 11, 3, 13, 7, 5, 2, 17, 2, 19, 5, 7, 11, 23, 3, 2, 13, 3, 7, 29, 5, 31, 5, 11, 17, 7, 2, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 2, 2, 17, 13, 53, 3, 11, 7, 19, 29, 59, 5, 61, 31, 7, 3, 13, 11, 67, 17, 23, 7, 71, 2, 73, 37, 2

Offset: 1

Author

Rémy Sigrist, Apr 23 2021

Keywords

• nonn

Comments

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

Examples

			See Links section.
		

Links

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

Crossrefs

Cf. A006530, A182318, A338669.

Programs

PARI

a(n) = if (n==1, 1, my (f=factor(n), w=#f~); if (f[w,2]==1, f[w,1], a(f[w,2])))

Formula

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

a(n) = a(A053585(n)).