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

1,1

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A343339 A157239 A158003 * A172354 A295130 A257765

Adjacent sequences: A225710 A225711 A225712 * A225714 A225715 A225716

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Status

approved