A346466 - OEIS

%I #15 Dec 04 2021 12:40:07

%S 1,1,2,1,4,1,6,1,2,1,10,1,12,1,2,1,16,1,18,1,2,1,22,1,4,1,2,1,28,1,30,

%T 1,2,1,1,1,36,1,2,1,40,1,42,1,4,1,46,1,6,1,2,1,52,1,1,1,2,1,58,1,60,1,

%U 2,1,4,1,66,1,2,1,70,1,72,1,2,1,1,1,78,1,2,1,82,1,4,1,2,1,88,1,6,1,2,1,1,1,96,1,2,1,100,1,102,1,4

%N The least common multiple of all divisors d of n-1 such that d+1 is a prime divisor of n; a(1) = 1.

%H Antti Karttunen, <a href="/A346466/b346466.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

%F a(n) = LCM_{p-1|n-1, p|n, p prime} (p-1).

%F a(n) = p-1 for prime powers n = p^e, e >= 1; a(n) = 1 for any even n = 2k. - _M. F. Hasler_, Nov 23 2021

%e From _M. F. Hasler_, Nov 23 2021: (Start)

%e For n = 2, the only prime factor of n is p = 2, and p-1 = 1 divides n-1 = 1, therefore a(2) = LCM { 1 } = 1.

%e For n = 35, the prime factors of n are p = 5 and p = 7; but neither 5-1 = 4 nor 7-1 = 6 divides n-1 = 34, therefore a(35) = LCM {} = 1. (End)

%o (PARI) A346466(n) = lcm(apply(p->if((n-1)%(p-1),1,(p-1)), factor(n)[, 1]));

%o (PARI) A346466(n) = if(1==n,n,my(m=1); fordiv(n-1,d,if(isprime(1+d)&&!(n%(1+d)),m = lcm(m,d))); (m));

%o (PARI) apply( {A346466(n)=lcm([p-1|p<-factor(n)[,1],(n-1)%(p-1)==0])}, [1..99]) \\ _M. F. Hasler_, Nov 23 2021

%Y Cf. also A173614, A346467.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jul 19 2021