A268336 a(n) = A174824(n)/n, where A174824(n) = lcm(A002322(n), n) and A002322(n) is the Carmichael lambda function (also known as the reduced totient function or the universal exponent of n).

1, 1, 2, 1, 4, 1, 6, 1, 2, 2, 10, 1, 12, 3, 4, 1, 16, 1, 18, 1, 2, 5, 22, 1, 4, 6, 2, 3, 28, 2, 30, 1, 10, 8, 12, 1, 36, 9, 4, 1, 40, 1, 42, 5, 4, 11, 46, 1, 6, 2, 16, 3, 52, 1, 4, 3, 6, 14, 58, 1, 60, 15, 2, 1, 12, 5, 66, 4, 22, 6, 70, 1, 72, 18, 4, 9, 30, 2, 78, 1, 2

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 01 2016

Keywords

• nonn
• easy

Crossrefs

Cf. A002322, A068563, A124240, A174824.

Programs

Magma

[1] cat [Lcm(n, CarmichaelLambda(n))/n: n in [2..100]]: // Feb 03 2016

Mathematica

Table[LCM[n, CarmichaelLambda@ n]/n, {n, 100}] (* Michael De Vlieger, Feb 03 2016, after T. D. Noe at A174824 *)

PARI

a(n)=my(ps); ps=factor(n)[, 1]~; m = n; for(k=1, #ps, m=lcm(m, ps[k]-1)); m/n \\ Michel Marcus, Feb 21 2016

PARI

apply( {A268336(n)=lcm(lcm([p-1|p<-factor(n)[,1]]),n)/n}, [1..99]) \\ [...] = znstar(n)[2], but 3x faster. - M. F. Hasler, Nov 13 2019

Formula

a(n) = A174824(n)/n.

a(A124240(n)) = 1. - Michel Marcus, Feb 21 2016

Extensions

More terms from Vincenzo Librandi, Feb 03 2016