A225709 Composite squarefree numbers n such that p(i)-9 divides n+9, where p(i) are the prime factors of n.

15, 21, 33, 35, 39, 55, 77, 91, 119, 143, 195, 231, 255, 299, 455, 551, 651, 663, 715, 935, 1131, 1155, 1419, 2015, 2035, 2431, 3003, 3111, 3927, 4611, 5451, 7215, 7735, 8151, 8671, 9191, 10455, 11571, 15015, 15477, 16511, 18343, 18615, 23541, 24871, 25415, 28391

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Example

Prime factors of 16511 are 11, 19 and 79. We have that (16511+9)/(11-9) = 8260, (16511+9)/(19-9) = 1652 and (16511+9)/(79-9) = 236.

Maple

with(numtheory); A225709:=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: A225709(10^9, 9);

Mathematica

t = {}; n = 0; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n + 9, p - 9]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

Crossrefs

Cf. A208728, A225702-A225708, A225710-A225720.

Sequence in context: A002557 A128907 A321644 * A020162 A046404 A198680

Adjacent sequences: A225706 A225707 A225708 * A225710 A225711 A225712

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Status

approved