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%I #20 May 10 2022 11:17:59
%S 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,1,
%T 0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,
%U 0,2,0,0,0,2,0,1,0,1,1,0,1,0,1,0,0,0,0,1,1,2,0,0,3,0,0,0,0,1,1,2,1,0,0,0,1
%N Irregularity index of prime(n): number of numbers k, 1 <= k <= (p-3)/2, such that p = prime(n) divides the numerator of the Bernoulli number B(2k).
%C Note offset is 2: only odd primes are considered.
%H Amiram Eldar, <a href="/A091888/b091888.txt">Table of n, a(n) for n = 2..10001</a>
%F 0 if p is a regular prime; > 0 if p is an irregular prime.
%t irregPrimeIndex[n_] := Block[{p = Prime[n], cnt = 0, k = 1}, While[ 2k + 2 < p, If[ Mod[ Numerator[ BernoulliB[ 2k]], p] == 0, cnt++]; k++]; cnt]; Array[ irregPrimeIndex, 105, 2] (* _Robert G. Wilson v_, Sep 20 2012 *)
%o (PARI) a(n)=sum(i=1,(prime(n)-1)/2,if(numerator(bernfrac(2*i))%prime(n),0,1)) \\ corrected by _Amiram Eldar_, May 10 2022
%Y Cf. A073277 (primes having irregularity index 2), A060975 (primes having irregularity index 3), A061576 (least prime having irregularity index n), A091887 (irregularity index of irregular prime A000928(n)).
%Y Cf. A027641/A027642, A000367/A002445, A000928.
%K nonn
%O 2,36
%A _T. D. Noe_ and _Benoit Cloitre_, Feb 09 2004
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