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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. 1

%I

%S 411,1,3,447,2,57,212,8,307,13,5,38,319,99,3310,70,4,242,132,50,73,17,

%T 192,12,133,3532,41,22231,999,43,172,68,83,11878,294,30,6,111,9,776,

%U 2059,922,818,46,1183,23,216,182,557,2010,1818,3323,945,512,568,76

%N 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 a(1) = 411 because 411^2+1 = 2 * 13 * 73 * 89 and 89 - (2 + 13 + 73) = 89 - 88 = 1.

%p A212710 := proc(n)

%p local fs,gpf,opf,k ;

%p for k from 1 do

%p fs := numtheory[factorset](k^2+1) ;

%p gpf := max(op(fs)) ;

%p opf := add( f,f=fs)-gpf ;

%p if gpf-opf = n then

%p return k;

%p end if;

%p end do:

%p end proc:

%p seq(A212710(n),n=1..50) ; # _R. J. Mathar_, Nov 14 2014

%t 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 (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 Cf. A182011, A014442, A193462.

%K nonn

%O 1,1

%A _Michel Lagneau_, May 24 2012

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Last modified January 20 15:10 EST 2021. Contains 340302 sequences. (Running on oeis4.)