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

%I A338668 #13 Apr 25 2021 15:11:29
%S A338668 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,
%T A338668 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,
%U A338668 19,29,59,5,61,31,7,3,13,11,67,17,23,7,71,2,73,37,2
%N A338668 a(n) is the rightmost prime number in prime tower factorization of n; a(1) = 1.
%C A338668 The prime tower factorization of a number is defined in A182318.
%H A338668 Rémy Sigrist, <a href="/A338668/b338668.txt">Table of n, a(n) for n = 1..10000</a>
%H A338668 Rémy Sigrist, <a href="/A338668/a338668.pdf">Illustration of initial terms</a>
%F A338668 a(n) <= n with equality iff n = 1 or n is a prime number.
%F A338668 a(n) = a(A053585(n)).
%e A338668 See Links section.
%o A338668 (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])))
%Y A338668 Cf. A006530, A182318, A338669.
%K A338668 nonn
%O A338668 1,2
%A A338668 _Rémy Sigrist_, Apr 23 2021