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A324977 Denominator(Bernoulli_{m-1}) / m, where m is the n-th Carmichael number. 3
26805565070, 76004922, 702286000198710990, 302278602666, 5360679390, 423023231634556544606744470770, 582934735516230690164248578, 106515855804560422705933720818, 8763422623117673428800595536306232967379299351012370, 9231375124608836430, 94422948020637332890056101961518875879389605546105043450762033482730 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is an integer, because an odd composite number m is a Carmichael number iff m divides the denominator of Bernoulli_{m-1} (by Korselt's criterion and the von Staudt-Clausen theorem). See Pomerance, Selfridge, & Wagstaff, page 1006, and Kellner & Sondow, section on Bernoulli numbers.

LINKS

Table of n, a(n) for n=1..11.

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.

Index entries for sequences related to Bernoulli numbers.

Index entries for sequences related to Carmichael numbers.

FORMULA

a(n) = A027642(A002997(n)-1)/A002997(n).

EXAMPLE

The 1st Carmichael number is 561, and the denominator of Bernoulli_560 is 15037922004270, so a(1) = 15037922004270 / 561 = 26805565070.

MATHEMATICA

carnum = Cases[Range[1, 100000, 2], n_ /; Mod[n, CarmichaelLambda[n]] == 1 && ! PrimeQ[n]];

Table[Denominator[BernoulliB[m - 1]]/m, {m, carnum}]

CROSSREFS

Cf. A027642, A002997.

Sequence in context: A017398 A017662 A120322 * A015414 A252839 A307760

Adjacent sequences:  A324974 A324975 A324976 * A324978 A324979 A324980

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Mar 28 2019

STATUS

approved

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Last modified May 21 15:06 EDT 2019. Contains 323443 sequences. (Running on oeis4.)