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 A225706 Composite squarefree numbers n such that p(i)-6 divides n+6, where p(i) are the prime factors of n. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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

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Last modified June 15 18:33 EDT 2021. Contains 345049 sequences. (Running on oeis4.)