

A130682


Numerator of generalized harmonic number H(p1,p^2) = Sum_{k=1..p1} 1/k^(p^2) divided by p^4 for prime p>3.


1




OFFSET

3,1


COMMENTS

The generalized harmonic number is H(n,m) = Sum_{k=1..n} 1/k^m. The numerator of the generalized harmonic number H(p1,p) is divisible by p^3 for prime p>3. See A119722(n). The numerator of the generalized harmonic number H(p1,p^2) is divisible by p^4 for prime p>3. In general, the numerator of the generalized harmonic number H(p1,p^k) is divisible by p^(k+2) for prime p>3.


LINKS



FORMULA

a(n) = Numerator[ Sum[ 1/k^(Prime[n]^2), {k,1,Prime[n]1} ] ] / Prime[n]^4 for n>2.


EXAMPLE

Prime[3] = 5.
a(3) = numerator[ 1 + 1/2^25 + 1/3^25 + 1/4^25 ] / 5^4 = 953962194872104906726451875/625 = 1526339511795367850762323.


MATHEMATICA

Table[ Numerator[ Sum[ 1/k^(Prime[n]^2), {k, 1, Prime[n]1} ] ] / Prime[n]^4, {n, 3, 10} ]


CROSSREFS

Cf. A119722 = Numerator of generalized harmonic number H(p1, p)= Sum[ 1/k^p, {k, 1, p1}] divided by p^3 for prime p>3.


KEYWORD

frac,nonn,uned,bref


AUTHOR



STATUS

approved



