A066636 a(n) = A066638(n)/n, where A066638(n) is the smallest power of a squarefree kernel of n that is a multiple of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 5, 1, 1, 1, 9, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 11, 5, 1, 1, 27, 1, 2, 1, 13, 1, 4, 1, 49, 1, 1, 1, 15, 1, 1, 7, 1, 1, 1, 1, 17, 1, 1, 1, 3, 1, 1, 3, 19, 1, 1, 1, 125, 1, 1, 1, 21, 1

Offset: 1

Author

Reinhard Zumkeller, Jan 09 2002

Keywords

• nonn
• look

Comments

a(n) is the least m such that the prime power exponents of m*n are all equal; see also A062760. - David James Sycamore, Jun 13 2024

Examples

			12 = 2^2*3^1 so m = 3 (3*12 = 36 = 2^2*3^2).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A007947, A051903, A066638.

Cf. A062760.

Programs

Mathematica

Array[Apply[Times, #2[[All, 1]]]^Max[#2[[All, -1]] ]/#1 & @@ {#, FactorInteger@ #} &, 85] (* Michael De Vlieger, Nov 20 2017 *)

PARI

A066638(n) = { if(n==1, return(1)); my(f=factor(n),me=vecmax(f[, 2])); (prod(i=1, #f~, f[i, 1])^me); }; \\ After Charles R Greathouse IV's code.
A066636(n) = (A066638(n)/n); \\ Antti Karttunen, Nov 20 2017

Formula

a(n) = (A007947(n)^A051903(n))/n. - Antti Karttunen, Nov 20 2017