

A309002


Multiplicative with a(p) = p^2 and a(p^e) = p^a(e) for any e > 1 and prime number p.


1



1, 4, 9, 16, 25, 36, 49, 512, 81, 100, 121, 144, 169, 196, 225, 65536, 289, 324, 361, 400, 441, 484, 529, 4608, 625, 676, 19683, 784, 841, 900, 961, 33554432, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 12800, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 589824
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

To compute a(n): square every prime number at leaf position in the prime tower factorization of n (the prime tower factorization of a number is defined in A182318).
For any n > 0, a(n) is the least k such that A308993(k) = n.


LINKS

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


FORMULA

A308993(a(n)) = n.
A185102(a(n)) = 1 + A185102(n) for any n > 1.
a(n) >= n^2 with equality iff n is cubefree (A004709).


EXAMPLE

See Links section.


PROG

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


CROSSREFS

Cf. A004709, A182318, A185102, A308993.
Sequence in context: A028820 A122683 A235597 * A328953 A328558 A072862
Adjacent sequences: A308999 A309000 A309001 * A309003 A309004 A309005


KEYWORD

nonn,mult


AUTHOR

Rémy Sigrist, Jul 05 2019


STATUS

approved



