%I #33 Nov 24 2021 09:22:15

%S 1,1,2,1,4,1,6,1,4,1,10,1,12,1,2,1,16,1,18,1,20,1,22,1,12,1,2,1,28,1,

%T 30,1,16,1,2,1,36,1,2,1,40,1,42,1,44,1,46,1,48,1,10,1,52,1,18,1,28,1,

%U 58,1,60,1,2,1,16,1,66,1,4,1,70,1,72,1,2,1,4,1,78,1,80,1,82,1,84,1,2,1,88,1,90,1,92,1,2,1,96

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

%C Original definition: a(n) is the least common multiple of p-1 computed over all primes p for which p-1 is a divisor of n-1; a(1) = 1.

%H Robert Israel, <a href="/A346467/b346467.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A002322(A027642(n-1)).

%F a(n) = A346466(n) * A346481(n).

%F For n > 1, a(n) = (n-1) / A346468(n).

%F a(n) = LCM { d | n-1; d+1 is prime }, where "|" means "divides". - _M. F. Hasler_, Nov 23 2021

%p f:= proc(n)

%p if n::even then return 1 fi;

%p ilcm(op(select(d -> isprime(d+1), numtheory:-divisors(n-1))));

%p end proc:

%p f(1):= 1:

%p map(f, [$1..200]); # _Robert Israel_, Aug 30 2021

%t {1}~Join~Array[CarmichaelLambda@ Denominator@ BernoulliB@ # &, 96] (* _Michael De Vlieger_, Jul 22 2021 *)

%o (PARI) A346467(n) = if(1==n,n,my(m=1); fordiv(n-1,d,if(isprime(1+d),m = lcm(m,d))); (m));

%o (PARI) apply( {A346467(n)=if(n>1, lcm([d|d<-divisors(n-1),isprime(d+1)]), 1)}, [1..99]) \\ _M. F. Hasler_, Nov 23 2021

%Y Cf. A002322, A027642, A173614, A346466, A346468, A346481.

%Y Cf. also A343979.

%K nonn

%O 1,3

%A _Antti Karttunen_ and _Thomas Ordowski_, Jul 22 2021