A180252 Numbers where all prime divisors are of the form k^2+1.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 37, 40, 50, 64, 68, 74, 80, 85, 100, 101, 125, 128, 136, 148, 160, 170, 185, 197, 200, 202, 250, 256, 257, 272, 289, 296, 320, 340, 370, 394, 400, 401, 404, 425, 500, 505, 512, 514

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A002496} p/(p-1) = Product_{k in A005574} (1 + 1/k^2) = 2.809865... - Amiram Eldar, Sep 27 2020

Example

a(17) = 74 because 74 = 2*37 = (1^2+1)*(6^2+1).

Maple

with(numtheory):T:=array(1..50):U:=array(1..1000):k:=1:for m from 1 to 300
  do:x:=m^2+1:if type(x, prime)=true then T[k]:=x:k:=k+1:else fi:od:for x from
  2 to 2000 do: B:=factorset(x):yy:=nops(B):A:=convert(T, set):if A intersect
  B = B then printf(`%d, `, x):else fi:od:

Mathematica

Select[Range@520, And @@ IntegerQ /@ Sqrt[FactorInteger[#][[All, 1]] - 1] &] (* Ivan Neretin, Aug 31 2016 *)

Crossrefs

Cf. A002496, A002522, A005574.

Sequence in context: A032937 A126684 A089653 * A191203 A216686 A114652

Adjacent sequences: A180249 A180250 A180251 * A180253 A180254 A180255

Keyword

nonn

Author

Michel Lagneau, Jan 20 2011

Status

approved