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

1,12

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007947, A051903, A066638.

Cf. A062760.

Sequence in context: A348969 A030380 A375932 * A137578 A200146 A319095

Adjacent sequences: A066633 A066634 A066635 * A066637 A066638 A066639

Keyword

nonn,look

Author

Reinhard Zumkeller, Jan 09 2002

Status

approved