A122148 Numerator of Sum[ (-1)^(k+1) * 1/p(k)^p(k), {k,1,n}], where p(k) = Prime[k].

1, 23, 71983, 59280758269, 16913492177093188294859, 5122675745984257357873512804013239827, 4237683625666802603266159755806379107958975382128522814879

Offset: 1

Author

Alexander Adamchuk, Aug 22 2006

Keywords

• frac
• nonn

Comments

C = Sum[ (-1)^(k+1) * 1/Prime[k]^Prime[k], {k,1,Infinity} ] = 1/2^2 - 1/3^3 + 1/5^5 - 1/7^7 + 1/11^11 - 1/13^13 + ... A122147[n] is a decimal expansion of C = 0.213281748700785698255627...

Examples

			a[n] / A076265[n] begins 1/4, 23/108, 71983/337500, ...
		

Crossrefs

Cf. A051674, A122147, A094289, A117579, A076265, A000040.

Programs

Mathematica

Table[Numerator[Sum[(-1)^(k+1)*1/Prime[k]^Prime[k],{k,1,n}]],{n,1,10}]

Formula

a(n) = Numerator[ Sum[ (-1)^(k+1) * 1/Prime[k]^Prime[k], {k,1,n} ] ].