A326579 - OEIS

A326579

a(n) = n*denominator(n*Bernoulli(n-1)) for n >= 1 and a(0) = 0.

0, 1, 2, 6, 4, 30, 6, 42, 8, 90, 10, 66, 12, 2730, 14, 30, 16, 510, 18, 798, 20, 2310, 22, 138, 24, 13650, 26, 54, 28, 870, 30, 14322, 32, 5610, 34, 210, 36, 1919190, 38, 78, 40, 13530, 42, 1806, 44, 2070, 46, 282, 48, 324870, 50, 1122, 52, 1590, 54, 43890, 56

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OFFSET

0,3

COMMENTS

Conjecture: For n>1: denominator(Bernoulli(n-1)) = n*denominator(n*Bernoulli(n-1)) <=> n is Korselt <=> n is prime or n is Carmichael.

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000

Bernd C. Kellner and Jonathan Sondow, On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-p digits, Integers 21 (2021), #A52, 21 pp.; arXiv preprint, arXiv:1902.10672 [math.NT], 2019-2021.

Carl Pomerance, J. L. Selfridge, and Samuel S. Wagstaff, Jr., The pseudoprimes to 25*10^9, Math. Comp., 35 (1980), 1003-1026.

Wikipedia, Carmichael numbers, Korselt's criterion.

FORMULA

a(2*n) = 2*n.

MAPLE

A326579 := n -> `if`(n = 0, 0, n*denom(n*bernoulli(n-1))): seq(A326579(n), n=0..56);

MATHEMATICA

a[n_] := n * Denominator[n * BernoulliB[n - 1]]; a[0] = 0; Array[a, 60, 0] (* Amiram Eldar, Apr 26 2024 *)

PROG

(PARI) a(n) = if (n, n*denominator(n*bernfrac(n-1)), 0); \\ Michel Marcus, Jul 19 2019

CROSSREFS

Cf. A326578, A326478, A326577, A027641/A027642 (Bernoulli), A002997 (Carmichael), A324050 (Korselt).

Sequence in context: A006233 A373985 A164020 * A057643 A073039 A373158

Adjacent sequences: A326576 A326577 A326578 * A326580 A326581 A326582

KEYWORD

nonn

AUTHOR

Peter Luschny, Jul 17 2019

STATUS

approved