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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
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 (list; graph; refs; listen; history; text; internal format)
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: A179129 A176598 A146075 * A187991 A090123 A055018

Adjacent sequences:  A212707 A212708 A212709 * A212711 A212712 A212713

KEYWORD

nonn

AUTHOR

Michel Lagneau, May 24 2012

STATUS

approved

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Last modified November 26 17:14 EST 2020. Contains 338641 sequences. (Running on oeis4.)