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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.
2
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, 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, 1, 4, 3, 10, 1, 24, 1, 2, 15, 4, 7, 6, 1, 16, 9, 2, 1, 12
OFFSET
1,4
COMMENTS
The prime tower factorization of a number is defined in A182318.
Sequence A338668 gives the rightmost prime number.
FORMULA
a(n) = 1 iff n = 1 or n is a prime number.
A106490(a(n)) = 1 + A106490(n) for any n > 1.
a^k(n) = 1 for k = A106490(n) (where a^k denotes the k-th iterate of a).
EXAMPLE
See Links section.
PROG
(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))) }
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 23 2021
STATUS
approved