A182011 -id:A182011 - cp's OEIS frontend

A182076 Smallest number k such that the difference between the greatest prime divisor of k and the product of the other distinct prime divisors equals n.

2, 3, 10, 5, 14, 7, 78, 33, 22, 11, 26, 13, 114, 51, 34, 17, 38, 19, 290, 69, 46, 23, 174, 145, 186, 87, 58, 29, 62, 31, 222, 185, 430, 111, 74, 37, 258, 123, 82, 41, 86, 43, 530, 141, 94, 47, 318, 265, 590, 159, 106, 53, 354, 295, 366, 177, 118, 59, 122, 61

Offset: 1

Michel Lagneau, Apr 10 2012

a(n) = n+1 if n+1 is prime.

			a(7) = 78 because the distinct prime divisors of 78 are {2, 3, 13} and 13 - 2*3 = 7.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A001221, A182011.

with(numtheory):for n from 1 to 60 do:ii:=0:for k from 2 to 200000 while(ii=0) do:x:=factorset(k):m:=nops(x): s:=product ('x[i] ', 'i'=1..m-1):if s+n = x[m]  then printf(`%d, `,k):ii:=1:else fi:od: od:

a(n)=my(t);for(k=n+1,4<Charles R Greathouse IV, Apr 11 2012

a(n)=my(p=nextprime(n+1));while(!issquarefree(p-n), p=nextprime(p+1));p*(p-n) \\ Charles R Greathouse IV, Apr 11 2012

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.

Original entry on oeis.org

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

Michel Lagneau, May 24 2012

nonn

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

Cf. A182011, A014442, A193462.

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

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 *)

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

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A182076 Smallest number k such that the difference between the greatest prime divisor of k and the product of the other distinct prime divisors equals n.

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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.

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