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Search: id:A069040
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| A069040 |
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Numbers n such that n divides the numerator of B(2n) (the Bernoulli numbers). |
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+0
4
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| 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 121, 125, 127, 131, 133, 137, 139, 143, 145, 149, 151, 155, 157, 161, 163, 167, 169, 173, 175, 179, 181
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equivalently, n is relatively prime to the denominator of B(2n). Equivalently, there are no primes p such that p divides n and p-1 divides 2n. These equivalences follow from the von Staudt-Clausen and Sylvester-Lipschitz theorems.
The listed terms are the same as those in A070191, but the sequences are not identical. (The similarity is mostly explained by the absence of multiples of 2, 3, and 55 from both sequences.) See A070192 and A070193 for the differences.
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REFERENCES
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G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed., Oxford Univ. Press, 1954.
I. Sh. Slavutskii, A note on Bernoulli numbers, Jour. of Number Theory 53 (1995), 309-310.
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MATHEMATICA
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testb[n_] := Select[First/@FactorInteger[n], Mod[2n, #-1]==0&]=={}; Select[Range[200], testb]
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CROSSREFS
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Adjacent sequences: A069037 A069038 A069039 this_sequence A069041 A069042 A069043
Sequence in context: A106571 A067291 A007310 this_sequence A070191 A135775 A066047
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 03 2002
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EXTENSIONS
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More information from Dean Hickerson (dean(AT)math.ucdavis.edu), Apr 26 2002
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