login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A346466
The least common multiple of all divisors d of n-1 such that d+1 is a prime divisor of n; a(1) = 1.
3
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, 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, 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
OFFSET
1,3
FORMULA
a(n) = LCM_{p-1|n-1, p|n, p prime} (p-1).
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
EXAMPLE
From M. F. Hasler, Nov 23 2021: (Start)
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.
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)
PROG
(PARI) A346466(n) = lcm(apply(p->if((n-1)%(p-1), 1, (p-1)), factor(n)[, 1]));
(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));
(PARI) apply( {A346466(n)=lcm([p-1|p<-factor(n)[, 1], (n-1)%(p-1)==0])}, [1..99]) \\ M. F. Hasler, Nov 23 2021
CROSSREFS
Cf. also A173614, A346467.
Sequence in context: A247339 A281071 A256908 * A258409 A060680 A057237
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 19 2021
STATUS
approved