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A309002

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

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

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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])))