A323136 a(n) is the least power of a prime that n reaches under the map x -> A070229(x), or -1 if we never reach a power of a prime.

1, 2, 3, 4, 5, 9, 7, 8, 9, 25, 11, 25, 13, 49, 25, 16, 17, 49, 19, 25, 49, 121, 23, 27, 25, 169, 27, 49, 29, 49, 31, 32, 121, 289, 49, 169, 37, 361, 169, 121, 41, 49, 43, 121, 121, 529, 47, 289, 49, 121, 289, 169, 53, 361, 121, 121, 361, 841, 59, 169, 61, 961

Offset: 1

Author

Rémy Sigrist, Jan 05 2019

Keywords

• nonn

Comments

The powers of primes correspond to A000961.

Apparently, a(n) > 0 for all n > 0.

Examples

			For n = 12:
- 12 = 2^2 * 3,
- A070229(12) = 12 + 3 = 15 = 3 * 5,
- A070229(15) = 15 + 5 = 20 = 2^2 * 5,
- A070229(20) = 20 + 5 = 25 = 5^5,
- hence a(12) = 25.
		

Links

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

Crossrefs

See A323135 for the corresponding number of iterations.

Cf. A000961, A006530, A070229.

Programs

PARI

a(n) = for (k=0, oo, if (omega(n) <= 1, return (n), my (f=factor(n)); n += f[#f~, 1]))

Formula

a(n) = n iff n belongs to A000961.

A006530(a(n)) >= A006530(n) when a(n) > 0.