A214391 Denominator of Sum_{k=1..n} 1/A045542(k).

3, 21, 168, 280, 210, 1365, 42315, 8463, 45136, 406224, 253890, 310310, 744744, 744744, 94582488, 661416, 110236, 21496020, 924328860, 7394630880, 894750336480, 5070251906720, 5704033395060, 6375096147420, 6375096147420, 2550038458968, 2550038458968

Offset

1,1

Comments

Goldbach-Euler: lim_{n -> oo} a(n)/A214391(n) = 1.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Lluís Bibiloni, Pelegrí Viader, and Jaume Paradís, On a Series of Goldbach and Euler, Amer. Math. Monthly, Vol. 113, No. 3 (2006), pp. 206-220.

Mathematica

seq[lim_] := Denominator[Accumulate[1 / Union[Table[m^k - 1, {k, 2, Log2[lim + 1]}, {m, 2, Surd[lim + 1, k]}] // Flatten]]]; seq[400] (* Amiram Eldar, Oct 14 2025 *)

Prog

(Haskell)
import Data.Ratio ((%), denominator)
a214391 n = a214391_list !! (n-1)
a214391_list = map denominator $ scanl1 (+) $ map (1 %) a045542_list

Crossrefs

Cf. A045542, A214390 (numerators).

Sequence in context: A262977 A361375 A371771 * A382369 A370284 A046637

Adjacent sequences: A214388 A214389 A214390 * A214392 A214393 A214394

Keyword

nonn,frac

Author

Reinhard Zumkeller, Jul 15 2012

Extensions

Name corrected by Amiram Eldar, Oct 14 2025

Status

approved