A052100 a(n) = lcm(n, phi(n), n - phi(n)).

0, 2, 6, 4, 20, 12, 42, 8, 18, 60, 110, 24, 156, 168, 840, 16, 272, 36, 342, 120, 252, 660, 506, 48, 100, 1092, 54, 336, 812, 1320, 930, 32, 8580, 2448, 9240, 72, 1332, 3420, 1560, 240, 1640, 420, 1806, 1320, 2520, 6072, 2162, 96, 294, 300, 31008, 2184, 2756

Offset: 1

Author

Labos Elemer, Jan 20 2000

Keywords

• nonn

Comments

If n is a power of a prime p, then a(n) = n*(p-1). - Robert Israel, May 20 2015

Examples

			For n=72, phi(72)=24, cototient(72)=48, a(72) = lcm(72,24,48) = 144.
For n=255, phi(255)=128, cototient(255)=127, a(255) = lcm(255,128,127) = 4145280.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A051953, A009262.

Programs

Maple

seq(ilcm(n, numtheory:-phi(n),n - numtheory:-phi(n)), n=1..100); # Robert Israel, May 20 2015

Mathematica

Table[LCM[n, EulerPhi[n], n - EulerPhi[n]], {n, 53}] (* Ivan Neretin, May 20 2015 *)

Formula

a(n) = lcm(n, A000010(n), A051953(n)).

For n=p prime, phi(p)=p-1, cototient(p)=p-1, a(p)=p(p-1)=A009262(p).

a(n) = n*A000010(n)*A051953(n)/A009195(n)^2. - Robert Israel, May 20 2015