A346467 a(n) is the least common multiple of the divisors d of n-1 such that d+1 is prime; a(1) = 1.

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, 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, 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

Offset: 1

Author

Antti Karttunen and Thomas Ordowski, Jul 22 2021

Keywords

• nonn

Comments

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.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Cf. also A343979.

Programs

Maple

f:= proc(n)
  if n::even then return 1 fi;
  ilcm(op(select(d -> isprime(d+1), numtheory:-divisors(n-1))));
end proc:
f(1):= 1:
map(f, [$1..200]); # Robert Israel, Aug 30 2021

Mathematica

{1}~Join~Array[CarmichaelLambda@ Denominator@ BernoulliB@ # &, 96] (* Michael De Vlieger, Jul 22 2021 *)

PARI

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

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

Formula

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

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

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

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