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A287620
a(n) = product, with multiplicity, of the prime numbers appearing at leaf positions in the prime tower factorization of n.
2
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).
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
KEYWORD
nonn,mult
AUTHOR
Rémy Sigrist, May 28 2017
STATUS
approved