cp's OEIS Frontend

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.

%I A323136 #13 Jan 12 2019 10:29:23
%S A323136 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,
%T A323136 169,27,49,29,49,31,32,121,289,49,169,37,361,169,121,41,49,43,121,121,
%U A323136 529,47,289,49,121,289,169,53,361,121,121,361,841,59,169,61,961
%N 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.
%C A323136 The powers of primes correspond to A000961.
%C A323136 Apparently, a(n) > 0 for all n > 0.
%H A323136 Rémy Sigrist, <a href="/A323136/b323136.txt">Table of n, a(n) for n = 1..10000</a>
%F A323136 a(n) = n iff n belongs to A000961.
%F A323136 A006530(a(n)) >= A006530(n) when a(n) > 0.
%e A323136 For n = 12:
%e A323136 - 12 = 2^2 * 3,
%e A323136 - A070229(12) = 12 + 3 = 15 = 3 * 5,
%e A323136 - A070229(15) = 15 + 5 = 20 = 2^2 * 5,
%e A323136 - A070229(20) = 20 + 5 = 25 = 5^5,
%e A323136 - hence a(12) = 25.
%o A323136 (PARI) a(n) = for (k=0, oo, if (omega(n) <= 1, return (n), my (f=factor(n)); n += f[#f~, 1]))
%Y A323136 See A323135 for the corresponding number of iterations.
%Y A323136 Cf. A000961, A006530, A070229.
%K A323136 nonn
%O A323136 1,2
%A A323136 _Rémy Sigrist_, Jan 05 2019