

A308993


Multiplicative with a(p) = 1 and a(p^e) = p^a(e) for any e > 1 and prime number p.


2



1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 2, 5, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 4, 7, 5, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 5, 2, 1, 1, 1, 4, 9, 1, 1, 2, 1, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

To compute a(n): remove every prime number at leaf position in the prime tower factorization of n (the prime tower factorization of a number is defined in A182318).


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Illustration of first terms


FORMULA

a(n) = 1 iff n is squarefree.
a^k(n) = 1 for any k >= A185102(n) (where a^k denotes the kth iterate of a).
a(n)^2 <= n with equality iff n is the square of some cubefree number (n = A004709(k)^2 for some k > 0).


EXAMPLE

See Links sections.


PROG

(PARI) a(n) = my (f=factor(n)); prod (i=1, #f~, f[i, 1]^if (f[i, 2]==1, 0, a(f[i, 2])))


CROSSREFS

Cf. A004709, A005117, A182318, A185102.
Sequence in context: A249739 A249740 A071773 * A000188 A162401 A324924
Adjacent sequences: A308990 A308991 A308992 * A308994 A308995 A308996


KEYWORD

nonn,mult


AUTHOR

Rémy Sigrist, Jul 04 2019


STATUS

approved



