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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.
6
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
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
KEYWORD
nonn,look
AUTHOR
Reinhard Zumkeller, Jan 09 2002
STATUS
approved