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A326578
a(n) = n^2*denominator(n*Bernoulli(n-1))/denominator(Bernoulli(n-1)) = n*A326478(n).
6
1, 2, 3, 16, 5, 36, 7, 64, 27, 100, 11, 144, 13, 196, 75, 256, 17, 324, 19, 400, 147, 484, 23, 576, 125, 676, 243, 784, 29, 900, 31, 1024, 363, 1156, 1225, 1296, 37, 1444, 507, 1600, 41, 1764, 43, 1936, 135, 2116, 47, 2304, 343, 2500, 867, 2704, 53, 2916, 3025
OFFSET
1,2
COMMENTS
Conjecture: If n is Carmichael then a(n) = n.
Are the fixed points of this sequence the numbers satisfying Korselt's criterion?
LINKS
FORMULA
a(prime(n)) = prime(n).
a(n) = n^2/gcd(n*N(n-1), D(n-1)), with N(k)/D(k) = B(k) the k-th Bernoulli number.
MAPLE
A326578 := n -> n*A326478(n): seq(A326578(n), n=1..55);
db := n -> denom(bernoulli(n)): nb := n -> numer(bernoulli(n)):
a := n -> n^2/igcd(n*nb(n-1), db(n-1)): seq(a(n), n=1..55);
MATHEMATICA
a[n_] := Module[{b = BernoulliB[n - 1]}, n^2 * Denominator[n * b] / Denominator[b]]; Array[a, 60] (* Amiram Eldar, Apr 26 2024 *)
PROG
(PARI) a(n) = n^2*denominator(n*bernfrac(n-1))/denominator(bernfrac(n-1)); \\ Michel Marcus, Jul 17 2019
CROSSREFS
Cf. A326478, A326579, A326577, A027641/A027642 (Bernoulli), A002997 (Carmichael), A324050 (Korselt).
Sequence in context: A351748 A190116 A088447 * A103390 A167761 A364813
KEYWORD
nonn
AUTHOR
Peter Luschny, Jul 16 2019
STATUS
approved