A225706 Composite squarefree numbers n such that p(i)-6 divides n+6, where p(i) are the prime factors of n.

6, 10, 14, 15, 21, 30, 35, 42, 70, 78, 105, 154, 170, 210, 357, 759, 1110, 6195, 42465, 43554, 61755, 94605, 106386, 146910, 189399, 229119, 276914, 453590, 924099, 1239870, 2407119, 3915714, 4404394, 4524074, 5819145, 7396394, 8324869, 23701854, 30242654, 33413919

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Example

Prime factors of 8324869 are 7, 19, 53 and 1181. We have that (8324869+6)/(7-6) = 8324875, (8324869+6)/(19-6) = 640375, (8324869+6)/(53-6) = 177125 and (8324869+6)/(1181-6) = 7085.

Maple

with(numtheory); A225706:=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: A225706(10^9, 6);

Mathematica

t = {}; n = 0; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n + 6, p - 6]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

Crossrefs

Cf. A208728, A225702-A225705, A225707-A225720.

Sequence in context: A046400 A100660 A088709 * A063078 A064452 A085647

Adjacent sequences: A225703 A225704 A225705 * A225707 A225708 A225709

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Extensions

Extended by T. D. Noe, May 17 2013

Status

approved