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A346467
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a(n) is the least common multiple of the divisors d of n-1 such that d+1 is prime; a(1) = 1.
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6
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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FORMULA
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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
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MAPLE
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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:
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MATHEMATICA
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{1}~Join~Array[CarmichaelLambda@ Denominator@ BernoulliB@ # &, 96] (* Michael De Vlieger, Jul 22 2021 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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