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Irregular triangle T(n,k) read by rows with 1 <= k <= A091887 even indices 2i such that n-th irregular prime p (A000928) divides the numerator of the Bernoulli numbers B_{2i} (A000367) with 0 <= 2i <= p-3.
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%I #5 Jun 23 2019 09:52:30

%S 32,44,58,68,24,22,130,62,110,84,164,100,84,20,156,88,292,280,186,300,

%T 100,174,200,382,126,240,366,196,130,94,194,292,336,338,400,86,270,

%U 486,222,52,90,92,22,592,522,20,174,338,428,80,226,236,242,554,48,224,408,502,628,32,12,200,378,290,514,260,732,220,330,628,544,744,102,66,868,162,418,520,820,156,166

%N Irregular triangle T(n,k) read by rows with 1 <= k <= A091887 even indices 2i such that n-th irregular prime p (A000928) divides the numerator of the Bernoulli numbers B_{2i} (A000367) with 0 <= 2i <= p-3.

%C First index T(n,1) in row n is A035112(n).

%e Triangle starts with

%e n = 1 => p = 37 divides the numerator of B_{32} = -7709321041217;

%e n = 2 => p = 59: B_{44};

%e n = 3 => p = 67: B_{58};

%e n = 4 => p = 101: B_{68};

%e n = 5 => p = 103: B_{24};

%e n = 6 => p = 131: B_{22};

%e n = 7 => p = 149: B_{130};

%e n = 8 => p = 157: B_{62}, B_{110};

%e n = 9 => p = 233: B_{84};

%e etc.

%p T:=[]:

%p for j from 2 to 168 do

%p p:=ithprime(j);

%p B:=[]:

%p for i from 1 to (p-3)/2 do

%p if type(numer(bernoulli(2*i))/p,integer) then B:=[op(B),2*i]: fi:

%p od:

%p T:=[op(T),op(B)];

%p od:

%p op(T);

%Y Cf. A000367, A000928, A035112, A060974, A060975, A073276, A073277, A091887.

%K nonn,tabf

%O 1,1

%A _Martin Renner_, Jun 23 2019