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A069040 Numbers n such that n divides the numerator of B(2n) (the Bernoulli numbers). +0
4
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)
OFFSET

1,2

COMMENT

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.

REFERENCES

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.

MATHEMATICA

testb[n_] := Select[First/@FactorInteger[n], Mod[2n, #-1]==0&]=={}; Select[Range[200], testb]

CROSSREFS

Sequence in context: A106571 A067291 A007310 this_sequence A070191 A135775 A066047

Adjacent sequences: A069037 A069038 A069039 this_sequence A069041 A069042 A069043

KEYWORD

nonn

AUTHOR

Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 03 2002

EXTENSIONS

More information from Dean Hickerson (dean.hickerson(AT)yahoo.com), Apr 26 2002

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Last modified December 15 00:47 EST 2009. Contains 170825 sequences.


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