A173751 a(n) = gcd(n, lcm_{p is a prime divisor of n} (p-1)) = gcd(n, A173614(n)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 5, 2, 3, 2, 1, 4, 1, 2, 3, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 4, 1, 2, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 3

Offset: 1

Author

José María Grau Ribas, Feb 23 2010

Keywords

• nonn

Comments

a(n) is divisor of A126864(n).

Examples

			84 = 2^2*3*7; lcm{p-1|p is prime and divisor of 84} = lcm{1,2,6} = 6; gcd(84,6) = 6 ==> a(84)=6.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000
• A. M. Oller-Marcen, On arithmetic numbers, arXiv preprint arXiv:1206.1823 [math.NT], 2012. From _N. J. A. Sloane_, Nov 25 2012

Crossrefs

Cf. A173614.

Programs

Mathematica

fa=FactorInteger; lcm[n_] := Module[{aux = 1, lon = Length[fa[n]]}, Do[aux = LCM[aux, (fa[n][[i]][[1]] - 1)], {i, lon}]; aux] a[n_] := GCD[lcm[n], n]; Table[a[n], {n, 1, 300}]

PARI

a(n)=gcd(n, lcm(apply(p->p-1, factor(n)[,1]))) \\ Andrew Howroyd, Aug 06 2018