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

Offset: 1

Author

Rémy Sigrist, Jul 05 2019

Keywords

• nonn
• mult

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.

Examples

			See Links section.
		

Links

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

Crossrefs

Cf. A004709, A182318, A185102, A308993.

Programs

PARI

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

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).