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

Author

Jonathan Vos Post, Apr 11 2006

Keywords

• easy
• frac
• nonn

Comments

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

Examples

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

Crossrefs

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

Programs

Mathematica

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

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).