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A326579 a(n) = n*denominator(n*Bernoulli(n-1)) for n >= 1 and a(0) = 0. 4
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 (list; graph; refs; listen; history; text; internal format)
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
Bernd C. Kellner and Jonathan Sondow, On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-p digits, arXiv:1902.10672 [math.NT], 2019.
C. Pomerance, J. L. Selfridge, and S. S. Wagstaff, Jr., The pseudoprimes to 25*10^9, Math. Comp., 35 (1980), 1003-1026.
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);
PROG
(PARI) a(n) = if (n, n*denominator(n*bernfrac(n-1)), 0); \\ Michel Marcus, Jul 19 2019
CROSSREFS
A326578, A326478, A326577, A027641/A027642 (Bernoulli), A002997 (Carmichael), A324050 (Korselt).
Sequence in context: A335049 A006233 A164020 * A057643 A073039 A322792
KEYWORD
nonn
AUTHOR
Peter Luschny, Jul 17 2019
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)