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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A208728, A225702, A225704-A225720.

Sequence in context: A339248 A219126 A289232 * A017793 A017740 A197193

Adjacent sequences: A225700 A225701 A225702 * A225704 A225705 A225706

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Status

approved