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 A225702 Composite squarefree numbers n such that p-2 divides n+2 for each prime p dividing n. 33
 273, 54943, 67303, 199393, 831283, 1097305, 1363723, 1569103, 1590433, 3199579, 3282433, 3503773, 5645563, 5659333, 9260053, 9733843, 9984115, 10738033, 16645363, 19229533, 32168743, 37759363, 38645233, 50806585, 53825497, 56451373, 58327423, 62207173 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE Prime factors of 1097305 are 5, 11, 71 and 281. We have that (1097305+2)/(5-2)= 365769, (1097305+2)/(11-2) = 121923, (1097305+2)/(71-2)= 15903 and (1097305+2)/(281-2) = 3933. MAPLE with(numtheory); A225702:=proc(i, j) local c, d, n, ok, p, t; for n from 2 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: A225702(10^9, 2); MATHEMATICA t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 2] > 0 && Union[Mod[n + 2, p - 2]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t PROG (PARI) is(n, f=factor(n))=if(#f[, 2]<3 || vecmax(f[, 2])>1 || f[1, 1]==2, return(0)); for(i=1, #f~, if((n+2)%(f[i, 1]-2), return(0))); 1 \\ Charles R Greathouse IV, Nov 05 2017 CROSSREFS Cf. A208728, A225703-A225720. Sequence in context: A210270 A351766 A321035 * A307537 A295455 A174771 Adjacent sequences: A225699 A225700 A225701 * A225703 A225704 A225705 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 November 30 19:14 EST 2022. Contains 358453 sequences. (Running on oeis4.)