A225703 Composite squarefree numbers n such that p(i)-3 divides n+3, where p(i) are the prime factors of n.

77, 2717, 3245, 18221, 30797, 37177, 46397, 51997, 56573, 61997, 111757, 128573, 149765, 158197, 263117, 264517, 314717, 437437, 475157, 617437, 667573, 683537, 701005, 718333, 834197, 864497, 902957, 904397, 929005, 945277, 1030237, 1096205, 1139653, 1188317

Offset: 1

Author

Paolo P. Lava, May 13 2013

Keywords

• nonn

Examples

			Prime factors of 37177 are 7, 47 and 113. We have that (37177+3)/(7-3) = 9295, (37177+3)/(47-3) = 845 and (37177+3)/(113-3) = 338.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..80

Crossrefs

Cf. A208728, A225702, A225704-A225720.

Programs

Maple

with(numtheory); A225703:=proc(i,j) local c, d, n, ok, p, t;
for n from 1 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;
if  not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end: A225703(10^9,3);

Mathematica

t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 3] > 0 && Union[Mod[n + 3, p - 3]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)