A287620 a(n) = product, with multiplicity, of the prime numbers appearing at leaf positions in the prime tower factorization of n.

1, 2, 3, 2, 5, 6, 7, 3, 2, 10, 11, 6, 13, 14, 15, 2, 17, 4, 19, 10, 21, 22, 23, 9, 2, 26, 3, 14, 29, 30, 31, 5, 33, 34, 35, 4, 37, 38, 39, 15, 41, 42, 43, 22, 10, 46, 47, 6, 2, 4, 51, 26, 53, 6, 55, 21, 57, 58, 59, 30, 61, 62, 14, 6, 65, 66, 67, 34, 69, 70, 71

Offset: 1

Author

Rémy Sigrist, May 28 2017

Keywords

• nonn
• mult

Comments

The prime tower factorization of a number is defined in A182318.

a(n) <= n.

a(n) = n iff n is squarefree (A005117).

a(n) is noncomposite iff n belongs to A164336.

This sequence is surjective; see A287621 for the least k such that a(k) = n.

For n>1, A001222(a(n)) = A064372(n).

Examples

			See illustration of the first terms in Links section.
		

Links

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

Crossrefs

Cf. A001222, A005117, A064372, A164336, A182318, A287621.

Programs

PARI

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

Formula

Multiplicative with:

- a(p) = p for any prime p,

- a(p^k) = a(k) for any prime p and k > 1.