A066575 LCM of numbers m such that 1 <= m <= n, m has a common factor with n, but m does not divide n.

1, 1, 1, 1, 1, 4, 1, 6, 6, 24, 1, 360, 1, 120, 180, 420, 1, 1680, 1, 5040, 1260, 5040, 1, 55440, 60, 55440, 2520, 720720, 1, 10810800, 1, 360360, 83160, 1441440, 2100, 73513440, 1, 24504480, 1081080, 2327925600, 1, 1396755360, 1, 465585120, 5405400, 465585120, 1, 32125373280, 420, 10708457760, 36756720, 53542288800, 1

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

Cf. A025487, A045763, A133995.

Sequence in context: A021028 A193529 A214561 * A070251 A134234 A207628

Adjacent sequences: A066572 A066573 A066574 * A066576 A066577 A066578

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