A347240 a(n) is the largest prime factor (A006530) of all terms encountered when iterating the map x -> A000593(x), when starting from x = n, but excluding the n itself. If n is a power of 2, then a(n) = 1. If 1 is never reached, then a(n) = -1.

1, 1, 2, 1, 3, 2, 2, 1, 13, 3, 3, 2, 7, 2, 3, 1, 13, 13, 5, 3, 2, 3, 3, 2, 31, 7, 5, 2, 5, 3, 2, 1, 3, 13, 3, 13, 19, 5, 7, 3, 7, 2, 11, 3, 13, 3, 3, 2, 19, 31, 13, 7, 5, 5, 13, 2, 5, 5, 5, 3, 31, 2, 13, 1, 7, 3, 17, 13, 3, 3, 13, 13, 37, 19, 31, 5, 3, 7, 5, 3, 19, 7, 7, 2, 5, 11, 5, 3, 13, 13, 7, 3, 2, 3, 5, 2, 19

Offset: 1

Author

Antti Karttunen, Aug 28 2021

Keywords

• nonn

Examples

			For n = 17, the iteration proceeds as follows 17 -> 18 (= 2*3*3), 18 -> 13 (13 is a prime), 13 -> 14 (= 2*7), 14 -> 8 (= 2*2*2), 8 -> 1. The largest prime factor present after the initial step is 13, thus a(17) = 13.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000593, A006530, A336361, A347241, A347242, A347243, A347244.

Cf. also A161942.

Programs

PARI

A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A000265(n) = (n >> valuation(n, 2));
A000593(n) = sigma(A000265(n));
A347240(n) = { my(m=1); while(n>1, n = A000593(n); m = max(m, A006530(n))); (m); };

Formula

a(n) = A347241(A000593(n)). - Antti Karttunen, Feb 10 2022