cp's OEIS Frontend

A196219 Numbers n such that n^2 is divisible by the sum of the distinct prime divisors of n^2 + 1.

%I A196219 #23 Oct 30 2018 10:31:02
%S A196219 7,18,187,378,1560,1683,1710,1719,4697,7788,8832,10693,21708,22968,
%T A196219 27378,28322,29032,30016,30635,32220,32368,33813,36725,41028,42444,
%U A196219 44733,45630,45985,50085,57768,69936,81639,86420,87116,92667,95418,96348,97185,114100
%N A196219 Numbers n such that n^2 is divisible by the sum of the distinct prime divisors of n^2 + 1.
%H A196219 Charles R Greathouse IV and Zak Seidov, <a href="/A196219/b196219.txt">Table of n, a(n) for n = 1..500</a> (1..100 from Levin)
%e A196219 1560 is in the sequence because the sum of the prime distinct divisors of 1560^2+1 is 17+37+53+73=180 and 1560^2 /180=13520.
%p A196219 with(numtheory):for k from 1 to 120000 do: y:=factorset(k^2+1): s:=sum(y[i],i=1..nops(y)):if irem(k^2,s)=0 then printf(`%d, `, k):else fi:od:
%t A196219 c=0;s={};Do[If[PowerMod[n,2,Plus@@First/@FactorInteger[n^2+1]]==0,AppendTo[s,n];c++;If[c==100,Break[]]],{n,2*10^6}];s (* _Zak Seidov_, Oct 14 2011 *)
%o A196219 (PARI) is(n)=my(f=factor(n^2+1)[,1]);n^2%sum(i=1,#f,f[i])==0 \\ _Charles R Greathouse IV_, Oct 25 2011
%Y A196219 Cf. A002522, A180278.
%K A196219 nonn
%O A196219 1,1
%A A196219 _Michel Lagneau_, Sep 29 2011