A144852 a(n) = number of distinct prime divisors (taken together) of numbers of the form 4x^2+1 for x<=10^n.

9, 87, 836, 8000, 78124, 766585, 7556731, 74771106, 741554656, 7366252759, 73261462211, 729280694469

Offset: 1

Author

Artur Jasinski & Bernhard Helmes (bhelmes(AT)gmx.de), Sep 22 2008

Keywords

• nonn

Comments

Primes of the form 4x^2+1 see A121326(n) = A002496(n+1).

Links

• Bernhard Helmes, Prime sieving on the polynomial f(n)=4n^2+1.

Crossrefs

Cf. A002383, A121326, A143835, A143868, A144848, A144850, A144851.

Programs

Mathematica

d = 10; l = 0; p = 4; c = {}; a = {}; Do[k = p x^2 + 1; b = Divisors[k]; Do[If[PrimeQ[b[[n]]], AppendTo[a, b[[n]]]], {n, 1, Length[b]}]; If[x == d, a = Union[a]; l = Length[a]; d = 10 d; Print[l]; AppendTo[c, l]], {x, 1, 10000}]; c (*Artur Jasinski*)

Extensions

Fixed broken link, corrected and extended to agree with website. - Ray Chandler, Jun 30 2015