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

1,1

Links

Table of n, a(n) for n=1..56.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A182011, A014442, A193462.

Sequence in context: A176598 A146075 A374270 * A187991 A090123 A055018

Adjacent sequences: A212707 A212708 A212709 * A212711 A212712 A212713

Keyword

nonn

Author

Michel Lagneau, May 24 2012

Status

approved