

A069040


Numbers n such that n divides the numerator of B(2n) (the Bernoulli numbers).


6



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
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OFFSET

1,2


COMMENTS

Equivalently, n is relatively prime to the denominator of B(2n). Equivalently, there are no primes p such that p divides n and p1 divides 2n. These equivalences follow from the von StaudtClausen and SylvesterLipschitz 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), 309310.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..300


MAPLE

A069040 := proc(n)
option remember;
if n=1 then
1;
else
for k from procname(n1)+1 do
if numer(bernoulli(2*k)) mod k = 0 then
return k;
end if;
end do:
end if;
end proc: # R. J. Mathar, Jan 06 2013


MATHEMATICA

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


CROSSREFS

Cf. A070191, A070192, A070193.
Sequence in context: A286265 A339911 A007310 * A070191 A231810 A314294
Adjacent sequences: A069037 A069038 A069039 * A069041 A069042 A069043


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Apr 03 2002


EXTENSIONS

More information from Dean Hickerson, Apr 26 2002


STATUS

approved



