|
| |
|
|
A125194
|
|
Numerator of generalized harmonic number H((p-1)/2,2p)= Sum[ 1/k^(2p), {k,1,(p-1)/2}] divided by p^2 for prime p>3.
|
|
0
| |
|
|
41, 1599366601, 10877829357646990581304675244472669289, 100935935338172297894217692920950359818733561, 9217176064595104612826996436899733706027947436610177335077693637792069056822883934927465549747441
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 3,1
|
|
|
COMMENTS
| Generalized harmonic number is H(n,m)= Sum[ 1/k^m, {k,1,n} ]. The numerator of generalized harmonic number H(p-1,2p) is divisible by p^2 for prime p>3 (see A120290(n)). The numerator of generalized harmonic number H((p-1)/2,2p) is divisible by p^2 for prime p>3.
|
|
|
LINKS
| Eric Weisstein, Link to a section of The World of Mathematics: Harmonic number.
Eric Weisstein, Link to a section of The World of Mathematics: Wolstenholme's Theorem.
|
|
|
FORMULA
| a(n) = Numerator[ Sum[ 1/k^(2*Prime[n]), {k,1,(Prime[n]-1)/2} ]] / Prime[n]^2 for n>2.
|
|
|
EXAMPLE
| Prime[3] = 5.
a(3) = Numerator[ 1 + 1/2^10 ] / 5^2 = 1025 / 25 = 41.
|
|
|
MATHEMATICA
| Do[p=Prime[k]; f=0; Do[f=f+1/n^(2p); g=Numerator[f]; If[IntegerQ[g/(p)^2], Print[{p, g/p^2}]], {n, 1, (p-1)/2}], {k, 1, 100}]
|
|
|
CROSSREFS
| Cf. A120290, A119722, A001008, A007406, A007408, A007410.
Sequence in context: A112550 A114927 A087512 * A095189 A023932 A022074
Adjacent sequences: A125191 A125192 A125193 * A125195 A125196 A125197
|
|
|
KEYWORD
| frac,nonn
|
|
|
AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 13 2007
|
| |
|
|
