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A218755 Denominators of Bernoulli numbers which are == 6 (mod 9). 2

%I

%S 6,42,330,510,690,798,870,1410,1518,1590,1770,1806,2490,3102,3210,

%T 3318,3894,4110,4326,4470,4686,5010,5190,5370,5478,6486,6810,7062,

%U 7890,8070,8142,8646,8790,9366,9510,10410,10770,11022

%N Denominators of Bernoulli numbers which are == 6 (mod 9).

%C The sequence contains the elements of A090801 which are == 6 (mod 9).

%C Conjecture: all first differences 36, 288, 180, 180,... of the sequence are multiples of 36.

%C The conjecture is true, since elements of A090801 are 2 mod 4. - _Charles R Greathouse IV_, Nov 22 2012

%H Charles R Greathouse IV, <a href="/A218755/b218755.txt">Table of n, a(n) for n = 1..10000</a>

%t Take[Union[Select[Denominator[BernoulliB[Range[1000]]],Mod[#,9]==6&]],60] (* _Harvey P. Dale_, Nov 28 2012 *)

%o (PARI) is(n)=if(n%36-6, 0, my(f=factor(n)); if(vecmax(f[, 2])>1, return(0)); fordiv(lcm(apply(k->k-1, f[, 1])), k, if(isprime(k+1) && n%(k+1), return(0))); 1) \\ _Charles R Greathouse IV_, Nov 26 2012

%Y Second subset of the Bernoulli denominators: A090801 which are == 3 (mod 9).

%K nonn,easy

%O 1,1

%A _Paul Curtz_, Nov 05 2012

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Last modified June 14 16:19 EDT 2021. Contains 345037 sequences. (Running on oeis4.)