A099208 In canonical prime-factorization of n replace prime(k)^e with prime(k+e-1).

1, 2, 3, 3, 5, 6, 7, 5, 5, 10, 11, 9, 13, 14, 15, 7, 17, 10, 19, 15, 21, 22, 23, 15, 7, 26, 7, 21, 29, 30, 31, 11, 33, 34, 35, 15, 37, 38, 39, 25, 41, 42, 43, 33, 25, 46, 47, 21, 11, 14, 51, 39, 53, 14, 55, 35, 57, 58, 59, 45, 61, 62, 35, 13, 65, 66, 67, 51, 69, 70, 71, 25, 73, 74

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(prime(k)^e) = prime(k+e-1).

a(n) = n iff n is squarefree.

a(n) <= n.

A099209(n) = a(a(n)).

a(A005117(n)) = A005117(n).

a(A013929(n)) < A013929(n).

Example

a(75) = a(3^1 * 5^2) = prime(2 + 0) * prime(3 + 1) = 3*7 = 21.

Mathematica

a[n_] := Times @@ (FactorInteger[n] /. {p_Integer, e_Integer} -> Prime[ PrimePi[p] + e - 1]); a[1] = 1; Array[a, 100] (* Jean-François Alcover, Dec 07 2016 *)

Prog

(PARI) a(n) = { my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); prime(primepi(p) + e - 1)) } \\ Andrew Howroyd, Nov 11 2025

Crossrefs

Cf. A005117, A013929, A099209.

Sequence in context: A003967 A349390 A099209 * A331299 A052274 A353842

Adjacent sequences: A099205 A099206 A099207 * A099209 A099210 A099211

Keyword

nonn,mult

Author

Reinhard Zumkeller, Oct 05 2004

Status

approved