A118056 Denominator of Sum_{i=1..n} 1/(s(i)^s(i)) where s(i) = i-th semiprime.

256, 186624, 99179645184, 3874204890000000000, 42041202325478752505760000000000, 131378757267121101580500000000000000, 2921293509192991260690562210500000000000000, 60877138794045118308172632628761960350250724033554048000000000000000

Offset

1,1

Comments

Semiprime analog of A076265. Fractions are 1/256, 733/186624, 389546509/99179645184, 15216660895232989/3874204890000000000, 165124648173861912289213141201/42041202325478752505760000000000, 516014525543318775927975356319557/131378757267121101580500000000000000, 11473924061057077116469420939475877122177 / 2921293509192991260690562210500000000000000, 239106294995420151295311285049507497083520504633431021289373163777 / 60877138794045118308172632628761960350250724033554048000000000000000.

Links

Table of n, a(n) for n=1..8.

Formula

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

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

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

Example

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

Mathematica

Denominator[Accumulate[1/#^#&/@Select[Range[30], PrimeOmega[#]==2&]]] (* Harvey P. Dale, Feb 15 2012 *)

Crossrefs

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

Sequence in context: A333585 A185924 A013997 * A185563 A220302 A013833

Adjacent sequences: A118053 A118054 A118055 * A118057 A118058 A118059

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, Apr 11 2006

Extensions

Corrected by Harvey P. Dale, Feb 15 2012

Status

approved