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

1,2

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).

Links

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

Rémy Sigrist, Illustration of the first terms

Formula

Multiplicative with:

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

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

Example

See illustration of the first terms in Links section.

Prog

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

Crossrefs

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

Sequence in context: A327937 A259445 A080979 * A304491 A277803 A062789

Adjacent sequences: A287617 A287618 A287619 * A287621 A287622 A287623

Keyword

nonn,mult

Author

Rémy Sigrist, May 28 2017

Status

approved