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%I #14 May 17 2013 15:12:25
%S 14,22,35,55,65,77,102,110,143,165,182,221,455,494,665,935,1001,1173,
%T 1430,2717,2795,4505,4526,4862,5957,6479,11526,27521,30485,34661,
%U 35126,45917,49715,52910,53846,81686,90574,106865,113477,118745,139073,140822,147095
%N Composite squarefree numbers n such that p(i)-10 divides n+10, where p(i) are the prime factors of n.
%e Prime factors of 34661 are 11, 23 and 137. We have that (34661+10)/(11-10) = 34671, (34661+10)/(23-10) = 2667 and (34661+10)/(137-10) = 273.
%p with(numtheory); A225710:=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: A225710(10^9,10);
%t t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n + 10, p - 10]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* _T. D. Noe_, May 17 2013 *)
%Y Cf. A208728, A225702-A225709, A225711-A225720.
%K nonn
%O 1,1
%A _Paolo P. Lava_, May 13 2013
%E Extended by _T. D. Noe_, May 17 2013