A173751 - OEIS

%I #22 Aug 07 2018 11:40:09

%S 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,

%T 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,

%U 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

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

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

%H Andrew Howroyd, <a href="/A173751/b173751.txt">Table of n, a(n) for n = 1..10000</a>

%H A. M. Oller-Marcen, <a href="http://arxiv.org/abs/1206.1823">On arithmetic numbers</a>, arXiv preprint arXiv:1206.1823 [math.NT], 2012. From _N. J. A. Sloane_, Nov 25 2012

%e 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.

%t 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}]

%o (PARI) a(n)=gcd(n, lcm(apply(p->p-1, factor(n)[,1]))) \\ _Andrew Howroyd_, Aug 06 2018

%Y Cf. A173614.

%K nonn

%O 1,6

%A _José María Grau Ribas_, Feb 23 2010