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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.

%I A066636 #21 Jun 28 2024 14:01:59
%S A066636 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,
%T A066636 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,
%U A066636 1,1,17,1,1,1,3,1,1,3,19,1,1,1,125,1,1,1,21,1
%N 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.
%C A066636 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
%H A066636 Antti Karttunen, <a href="/A066636/b066636.txt">Table of n, a(n) for n = 1..16384</a>
%F A066636 a(n) = (A007947(n)^A051903(n))/n. - _Antti Karttunen_, Nov 20 2017
%e A066636 12 = 2^2*3^1 so m = 3 (3*12 = 36 = 2^2*3^2).
%t A066636 Array[Apply[Times, #2[[All, 1]]]^Max[#2[[All, -1]] ]/#1 & @@ {#, FactorInteger@ #} &, 85] (* _Michael De Vlieger_, Nov 20 2017 *)
%o A066636 (PARI)
%o A066636 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.
%o A066636 A066636(n) = (A066638(n)/n); \\ _Antti Karttunen_, Nov 20 2017
%Y A066636 Cf. A007947, A051903, A066638.
%Y A066636 Cf. A062760.
%K A066636 nonn,look
%O A066636 1,12
%A A066636 _Reinhard Zumkeller_, Jan 09 2002