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A091888
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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).
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1
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,36
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COMMENTS
| Note offset is 2: only odd primes are considered.
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FORMULA
| 0 if p is a regular prime; > 0 if p is an irregular prime
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MATHEMATICA
| Table[p=Prime[i]; cnt=0; k=1; While[2k<=p-3, If[Mod[Numerator[BernoulliB[2k]], p]==0, cnt++ ]; k++ ]; cnt, {i, 2, 151}]
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PROG
| (PARI) a(n)=sum(i=1, (n-1)/2, if(numerator(bernfrac(2*i))%n, 0, 1))
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CROSSREFS
| 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)).
Cf. A027641/A027642, A000367/A002445, A000928.
Sequence in context: A005926 A089803 A089811 * A083928 A074038 A204843
Adjacent sequences: A091885 A091886 A091887 * A091889 A091890 A091891
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com) and Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 09 2004
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