A112622 If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = product_{p|n} b(p,n)^b(p,n).

1, 1, 1, 4, 1, 1, 1, 27, 4, 1, 1, 4, 1, 1, 1, 256, 1, 4, 1, 4, 1, 1, 1, 27, 4, 1, 27, 4, 1, 1, 1, 3125, 1, 1, 1, 16, 1, 1, 1, 27, 1, 1, 1, 4, 4, 1, 1, 256, 4, 4, 1, 4, 1, 27, 1, 27, 1, 1, 1, 4, 1, 1, 4, 46656, 1, 1, 1, 4, 1, 1, 1, 108, 1, 1, 4, 4, 1, 1, 1, 256, 256, 1, 1, 4, 1, 1, 1, 27, 1, 4, 1, 4, 1, 1, 1, 3125, 1, 4, 4, 16, 1, 1, 1, 27, 1

Offset

1,4

Comments

a(1) = 1 (empty product).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Example

45 = 3^2 * 5^1. So a(45) = 2^2 * 1^1 = 4.
72 = 2^3 * 3^2. So a(72) = 3^3 * 2^2 = 108.

Mathematica

f[n_] := Block[{fi = Last@Transpose@FactorInteger@n}, Times @@ (fi^fi)]; Rest@Array[f, 93] (* Robert G. Wilson v *)

Prog

(PARI) a(n)=local(v, r, i); v=factorint(n); r=1; for(i=1, matsize(v)[1], r*=v[i, 2]^v[i, 2]); r (Herrgesell)

Crossrefs

Cf. A112621, A112624.

Sequence in context: A348989 A362297 A354358 * A183104 A183102 A178649

Adjacent sequences: A112619 A112620 A112621 * A112623 A112624 A112625

Keyword

nonn,mult

Author

Leroy Quet, Dec 25 2005

Extensions

More terms from Robert G. Wilson v and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 27 2005

Corrected the starting offset, data section extended to 105 terms - Antti Karttunen, May 28 2017

Status

approved