A118055 Numerator of Sum_{i=1..n} 1/(s(i)^s(i)) where s(i) = i-th semiprime.

1, 733, 389546509, 15216660895232989, 165124648173861912289213141201, 516014525543318775927975356319557, 11473924061057077116469420939475877122177

Offset

1,2

Comments

Semiprime analog of A117579. Fractions are 1/256, 733/186624, 389546509/99179645184, 15216660895232989/3874204890000000000, 165124648173861912289213141201/42041202325478752505760000000000, 516014525543318775927975356319557/131378757267121101580500000000000000, 11473924061057077116469420939475877122177 / 2921293509192991260690562210500000000000000, 239106294995420151295311285049507497083520504633431021289373163777 / 6087713879404511830817263262876196035025072.

Links

Table of n, a(n) for n=1..7.

Formula

a(n) = Numerator of Sum_{i=1..n} 1/(semiprime(i)^semiprime(i)).

a(n) = Numerator of Sum_{i=1..n} 1/(A001358(i)^A001358(i)).

a(n) = Numerator of Sum_{i=1..n} 1/A114850(n).

Example

a(2) = 733 because (1/semiprime(1)^semiprime(1)) + (1/semiprime(2)^semiprime(2))
= (1/256) + (1/46656) = 733/186624.

Mathematica

Numerator[Accumulate[1/#^#&/@Select[Range[25], PrimeOmega[#]==2&]]] (* Harvey P. Dale, Aug 09 2012 *)

Crossrefs

Denominators = A118055. Cf. A001358, A051674, A114850, A117579.

Sequence in context: A220625 A260035 A033529 * A025356 A025348 A126556

Adjacent sequences: A118052 A118053 A118054 * A118056 A118057 A118058

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, Apr 11 2006

Status

approved