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A338669 The prime tower factorization of a(n) is obtained by replacing the rightmost prime number by 1 in the prime tower factorization of n; a(1) = 1.

%I A338669 #15 Apr 25 2021 15:11:46
%S A338669 1,1,1,2,1,2,1,2,3,2,1,4,1,2,3,4,1,6,1,4,3,2,1,8,5,2,3,4,1,6,1,2,3,2,
%T A338669 5,12,1,2,3,8,1,6,1,4,9,2,1,16,7,10,3,4,1,6,5,8,3,2,1,12,1,2,9,4,5,6,
%U A338669 1,4,3,10,1,24,1,2,15,4,7,6,1,16,9,2,1,12
%N A338669 The prime tower factorization of a(n) is obtained by replacing the rightmost prime number by 1 in the prime tower factorization of n; a(1) = 1.
%C A338669 The prime tower factorization of a number is defined in A182318.
%C A338669 Sequence A338668 gives the rightmost prime number.
%H A338669 Rémy Sigrist, <a href="/A338669/b338669.txt">Table of n, a(n) for n = 1..10000</a>
%H A338669 Rémy Sigrist, <a href="/A338668/a338668.pdf">Illustration of initial terms</a>
%F A338669 a(n) = 1 iff n = 1 or n is a prime number.
%F A338669 A106490(a(n)) = 1 + A106490(n) for any n > 1.
%F A338669 a^k(n) = 1 for k = A106490(n) (where a^k denotes the k-th iterate of a).
%e A338669 See Links section.
%o A338669 (PARI) a(n) = { if (n==1, 1, my (f=factor(n), w=#f~, p=f[w,1], e=f[w,2]); if (e==1, n/p, n*p^(a(e)-e))) }
%Y A338669 Cf. A106490, A182318, A338668.
%K A338669 nonn
%O A338669 1,4
%A A338669 _Rémy Sigrist_, Apr 23 2021