A118063 Denominator of Sum_{i=1..n} 1/(t(i)^t(i)) where t(i) = i-th 3-almost prime.

16777216, 4458050224128, 1259085058409489202413568, 15738563230118615030169600000000000000000000, 46496637333593157266125580467610571799579852800000000000000000000

Offset

1,1

Comments

3-almost prime analog of A076265. (Semiprime analog of A076265 is A118056.) Fractions are 1/16777216, 265721/4458050224128, 75047458863267833/1259085058409489202413568, 938093235790847912650094635296999121 / 15738563230118615030169600000000000000000000, 2771420766426289313598405374054613260285749630619149892803 / 46496637333593157266125580467610571799579852800000000000000000000.

Links

Table of n, a(n) for n=1..5.

Formula

a(n) = Denominator of Sum_{i=1..n} 1/(3almostprime(i)^3almostprime(i)).

a(n) = Denominator of Sum_{i=1..n} 1/(A014612(i)^A014612(i)).

a(n) = Denominator of Sum_{i=1..n} 1/A114967(n).

Example

a(2) = 4458050224128 because (1/A014612(1)^A014612(1)) + (1/A014612(2)^A014612(2))= (1/(8^8)) + (1/(12^12)) = (1/16777216) + (1/8916100448256) = 265721/4458050224128.

Mathematica

Accumulate[1/#^#&/@Select[Range[30], PrimeOmega[#]==3&]]//Denominator (* Harvey P. Dale, Apr 05 2020 *)

Crossrefs

Numerators = A118062. Cf. A001358, A014612, A051674, A114850, A114967, A117579, A118056.

Sequence in context: A010812 A016968 A017040 * A017124 A114967 A017220

Adjacent sequences: A118060 A118061 A118062 * A118064 A118065 A118066

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, Apr 11 2006

Status

approved