A287621 -id:A287621 - cp's OEIS frontend

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

Rémy Sigrist, May 28 2017

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).

			See illustration of the first terms in Links section.

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

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

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

Multiplicative with:
- a(p) = p for any prime p,
- a(p^k) = a(k) for any prime p and k > 1.

cp's OEIS Frontend

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

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