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A212710 Smallest number k such that the difference between the greatest prime divisor of k^2+1 and the sum of the other prime distinct divisors equals n.

%I A212710 #9 Nov 14 2014 14:25:13
%S A212710 411,1,3,447,2,57,212,8,307,13,5,38,319,99,3310,70,4,242,132,50,73,17,
%T A212710 192,12,133,3532,41,22231,999,43,172,68,83,11878,294,30,6,111,9,776,
%U A212710 2059,922,818,46,1183,23,216,182,557,2010,1818,3323,945,512,568,76
%N A212710 Smallest number k such that the difference between the greatest prime divisor of k^2+1 and the sum of the other prime distinct divisors equals n.
%e A212710 a(1) = 411 because 411^2+1 = 2 * 13 * 73 * 89  and 89 - (2 + 13 + 73) = 89 - 88 = 1.
%p A212710 A212710 := proc(n)
%p A212710     local fs,gpf,opf,k ;
%p A212710     for k from 1 do
%p A212710         fs := numtheory[factorset](k^2+1) ;
%p A212710         gpf := max(op(fs)) ;
%p A212710         opf := add( f,f=fs)-gpf ;
%p A212710         if gpf-opf = n then
%p A212710             return k;
%p A212710         end if;
%p A212710     end do:
%p A212710 end proc:
%p A212710 seq(A212710(n),n=1..50) ; # _R. J. Mathar_, Nov 14 2014
%t A212710 lst={};Do[k=1;[While[!2*FactorInteger[k^2+1][[-1,1]]-Total[Transpose[FactorInteger[k^2+1]][[1]]]==n,k++]];AppendTo[lst,k],{n,0,60}];lst (* _Michel Lagneau_, Oct 28 2014 *)
%o A212710 (PARI) a(n) = {k = 1; ok = 0; while (!ok, f = factor(k^2+1); nbp = #f~; ok = (f[nbp, 1] - sum(i=1, nbp-1, f[i,1]) == n); if (!ok, k++);); k;} \\ _Michel Marcus_, Nov 09 2014
%Y A212710 Cf. A182011, A014442, A193462.
%K A212710 nonn
%O A212710 1,1
%A A212710 _Michel Lagneau_, May 24 2012