A225713 Composite squarefree numbers n such that p(i)+3 divides n-3, where p(i) are the prime factors of n.

195, 1235, 1443, 2915, 4403, 5883, 35203, 37635, 54723, 66563, 77503, 97555, 157403, 158403, 188355, 200203, 265411, 273003, 299715, 317203, 358179, 376995, 380373, 438243, 476003, 492803, 506883, 511683, 567633, 630203, 636803, 654951, 742269, 764463, 827203

Offset: 1

Author

Paolo P. Lava, May 13 2013

Keywords

• nonn

Examples

			Prime factors of 5883 are 3, 37 and 53. We have that (3+3)/(5883-3) = 980, (37+3)/(5883-3) = 147 and (53+3)/(5883-3) = 105.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A208728, A225702-A225712, A225714-A225720.

Programs

Maple

with(numtheory); A225713:=proc(i,j) local c, d, n, ok, p, t;
for n from 2 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: A225713(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} && Union[Mod[n - 3, p + 3]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)