A347241 a(1) = 1, and for n > 1, a(n) is the largest prime factor (A006530) of all terms encountered when iterating the map x -> A000593(x), when starting from x = n, and including the n itself. If 1 is never reached when starting from n, then a(n) = -1.

1, 2, 3, 2, 5, 3, 7, 2, 13, 5, 11, 3, 13, 7, 5, 2, 17, 13, 19, 5, 7, 11, 23, 3, 31, 13, 5, 7, 29, 5, 31, 2, 11, 17, 7, 13, 37, 19, 13, 5, 41, 7, 43, 11, 13, 23, 47, 3, 19, 31, 17, 13, 53, 5, 13, 7, 19, 29, 59, 5, 61, 31, 13, 2, 13, 11, 67, 17, 23, 7, 71, 13, 73, 37, 31, 19, 11, 13, 79, 5, 19, 41, 83, 7, 17, 43, 29

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 (when including the starting term also) is 17, thus a(17) = 17.
		

Links

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

Crossrefs

Cf. A000593, A006530, A161942, A336361, A347240, A347242.

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));
A347241(n) = { my(m=1); while(n>1, m = max(m, A006530(n)); n = A000593(n)); (m); };

Formula

a(n) = max(A006530(n), A347240(n)).