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

1, 2, 1, 4, 2, 6, 1, 2, 4, 10, 2, 12, 6, 4, 1, 16, 2, 18, 4, 6, 10, 22, 2, 4, 12, 2, 6, 28, 4, 30, 1, 10, 16, 12, 2, 36, 18, 12, 4, 40, 6, 42, 10, 4, 22, 46, 2, 6, 4, 16, 12, 52, 2, 20, 6, 18, 28, 58, 4, 60, 30, 6, 1, 12, 10, 66, 16, 22, 12, 70, 2, 72, 36, 4, 18, 30, 12, 78, 4, 2, 40, 82, 6

Offset: 2

Author

José María Grau Ribas, Feb 22 2010

Keywords

• nonn

Comments

The function psi(n) in the paper by Carlip et al. - R. J. Mathar, Aug 22 2012

Examples

			1425 = 3*5^2*19 => a(1425) = lcm(2,4,18) = 36.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..10000
• W. Carlip, E. Jacobson, and L. Somer, Pseudoprimes, perfect numbers and a problem of Lehmer, Fib. Quart. 36 (4) (1998) 361

Programs

Mathematica

a[n_] := {aux = 1; fa = FactorInteger[n]; len = Length[fa]; grau = Table[fa[[s]][[1]] - 1, {s, len}]; Do[aux = LCM[aux, grau[[i]]], {i, len}]; aux}[[1]]; Table[a[n], {n, 2, 40}]

PARI

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

Formula

Conjecture: a(n) = A002322(A007947(n)). - Velin Yanev, Feb 06 2021