OFFSET
1,6
COMMENTS
From Michael De Vlieger, Oct 30 2017: (Start)
a(p) = 1 and a(4) = 1, since all 1 <= m <= 4 either divide or are coprime to 4 and 4 is the smallest composite.
a(n) > 1 for composite n > 4.
There are 2 species of m. The first is m | n^e with e >= 2, the second is m that is the product of at least one prime p | n (A272618) and one prime q coprime to n (A272619). Both species of m are composite. We can simply look for composite m in the cototient of n such that m does not divide n.
(End)
This isn't a subsequence of A025487. - David A. Corneth, Oct 30 2017
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..1024
FORMULA
a(n) = lcm_{k} A133995(n,k). - Michael De Vlieger, Oct 30 2017
EXAMPLE
a(12) = 360 = lcm(8,9,10) as 8, 9 and 10 are the only numbers <= 12 which are not relatively prime to 12 nor do they divide 12.
MAPLE
for i from 1 to 100 do a := 1:for j from 1 to i do b := igcd(i, j); if(b>1 and b<j) then a := ilcm(a, j):end if:end do:c[i] := a; end do:q := seq(c[k], k=1..100);
MATHEMATICA
Table[Apply[LCM, Select[Range[2, n - 1], Nor[Divisible[n, #], CoprimeQ[n, #]] &] /. {} -> 1], {n, 53}] (* Michael De Vlieger, Oct 30 2017 *)
PROG
(PARI) A066575(n) = { my(m=1); for(k=1, n, if((n%k)&&(gcd(n, k)>1), m = lcm(m, k))); m; }; \\ Antti Karttunen, Oct 30 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Dec 19 2001
EXTENSIONS
More terms from Sascha Kurz, Mar 23 2002 and from Antti Karttunen, Oct 30 2017
STATUS
approved