A225718 - OEIS

%I #8 May 17 2013 11:38:29

%S 4958,51653,55583,271358,291338,789173,1379438,5430797,5785073,

%T 6350885,7159958,10532333,12822818,13892243,14809517,23831423,

%U 24547058,26734058,27391073,32079671,32673383,36126098,42560693,51346358,52177658,54949958

%N Composite squarefree numbers n such that p(i)+8 divides n-8, where p(i) are the prime factors of n.

%e Prime factors of 789173 are 7, 11, 37 and 277. We have that (789173-8)/(7+8) = 52611, (789173-8)/(11+8) = 41535, (789173-8)/(37+8) = 17537 and (789173-8)/(277+8) = 2769.

%p with(numtheory); A225718:=proc(i,j) local c, d, n, ok, p, t;

%p for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;

%p for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;

%p if  not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;

%p if ok=1 then print(n); fi; fi; od; end: A225718(10^9,-8);

%Y Cf. A208728, A225702-A225717, A225719, A225720.

%K nonn

%O 1,1

%A _Paolo P. Lava_, May 13 2013