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.

411, 1, 3, 447, 2, 57, 212, 8, 307, 13, 5, 38, 319, 99, 3310, 70, 4, 242, 132, 50, 73, 17, 192, 12, 133, 3532, 41, 22231, 999, 43, 172, 68, 83, 11878, 294, 30, 6, 111, 9, 776, 2059, 922, 818, 46, 1183, 23, 216, 182, 557, 2010, 1818, 3323, 945, 512, 568, 76

Offset: 1

Author

Michel Lagneau, May 24 2012

Keywords

• nonn

Examples

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

Crossrefs

Cf. A182011, A014442, A193462.

Programs

Maple

A212710 := proc(n)
    local fs,gpf,opf,k ;
    for k from 1 do
        fs := numtheory[factorset](k^2+1) ;
        gpf := max(op(fs)) ;
        opf := add( f,f=fs)-gpf ;
        if gpf-opf = n then
            return k;
        end if;
    end do:
end proc:
seq(A212710(n),n=1..50) ; # R. J. Mathar, Nov 14 2014

Mathematica

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 *)

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