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A069040
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Numbers k that divide the numerator of B(2k) (the Bernoulli numbers).
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6
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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
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OFFSET
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1,2
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COMMENTS
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Equivalently, k is relatively prime to the denominator of B(2k). Equivalently, there are no primes p such that p divides k and p-1 divides 2k. 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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LINKS
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MAPLE
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option remember;
if n=1 then
1;
else
for k from procname(n-1)+1 do
if numer(bernoulli(2*k)) mod k = 0 then
return k;
end if;
end do:
end if;
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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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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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