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 A180252 Numbers where all prime divisors are of the form k^2+1. 5

%I

%S 1,2,4,5,8,10,16,17,20,25,32,34,37,40,50,64,68,74,80,85,100,101,125,

%T 128,136,148,160,170,185,197,200,202,250,256,257,272,289,296,320,340,

%U 370,394,400,401,404,425,500,505,512,514

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

%H Ivan Neretin, <a href="/A180252/b180252.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

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

%p with(numtheory):T:=array(1..50):U:=array(1..1000):k:=1:for m from 1 to 300

%p do:x:=m^2+1:if type(x,prime)=true then T[k]:=x:k:=k+1:else fi:od:for x from

%p 2 to 2000 do: B:=factorset(x):yy:=nops(B):A:=convert(T, set):if A intersect

%p B = B then printf(`%d, `, x):else fi:od:

%t Select[Range@520, And @@ IntegerQ /@ Sqrt[FactorInteger[#][[All, 1]] - 1] &] (* _Ivan Neretin_, Aug 31 2016 *)

%Y Cf. A002496, A002522, A005574.

%K nonn

%O 1,2

%A _Michel Lagneau_, Jan 20 2011

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Last modified July 28 23:26 EDT 2021. Contains 346340 sequences. (Running on oeis4.)