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
Keywords
Examples
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.
Programs
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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);
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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 *)
Extensions
Extended by T. D. Noe, May 17 2013