|
Search: id:A069040
|
|
|
| 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
|
|
|
Search completed in 0.002 seconds
|
