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A225704 Composite squarefree numbers n such that p(i)-4 divides n+4, where p(i) are the prime factors of n. 3

%I

%S 6,10,14,15,30,35,66,266,455,806,4154,4686,6665,10370,16646,22781,

%T 31146,36305,72086,205871,246506,473711,570011,653666,733586,900581,

%U 904046,1422410,1941971,1969565,2023010,2807255,2821269,3009821,3043274,3355271,3880301

%N Composite squarefree numbers n such that p(i)-4 divides n+4, where p(i) are the prime factors of n.

%e Prime factors of 205871 are 29, 31 and 229. We have that (205871+4)/(29-4) = 8235, (205871+4)/(31-4) = 7625 and (205871+4)/(229-4) = 915.

%p with(numtheory); A225704:=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: A225704(10^9,4);

%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 + 4, p - 4]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* _T. D. Noe_, May 17 2013 *)

%Y Cf. A208728, A225702, A225703, A225705-A225720.

%K nonn

%O 1,1

%A _Paolo P. Lava_, May 13 2013

%E Extended by _T. D. Noe_, May 17 2013

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Last modified June 14 08:31 EDT 2021. Contains 345018 sequences. (Running on oeis4.)