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A225709
Composite squarefree numbers n such that p(i)-9 divides n+9, where p(i) are the prime factors of n.
3
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
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
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 13 2013
STATUS
approved