A225708 - OEIS

%I #16 May 17 2013 13:03:23

%S 10,22,55,70,154,190,322,385,442,595,682,2002,2737,3619,5530,14986,

%T 23782,24817,25102,26767,30430,31042,34762,37810,85462,106582,141427,

%U 171790,189727,225910,243217,248482,255142,272782,307090,381547,388102,471262,637849,798490

%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 381547 are 23, 53 and 313. We have that (381547+8)/(23-8)=25437, (381547+8)/(53-8)=8479 and (381547+8)/(313-8)=1251.

%p with(numtheory); A225708:=proc(i,j) local c, d, n, ok, p, t;

%p for n from 1 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: A225708(10^9,8);

%t t = {}; n = 0; While[Length[t] < 40, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n + 8, p - 8]] == {0}, AppendTo[t, n]]]; t (* _T. D. Noe_, May 17 2013 *)

%Y Cf. A208728, A225702-A225707, A225709-A225720.

%K nonn

%O 1,1

%A _Paolo P. Lava_, May 13 2013