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%I #15 Aug 17 2021 17:03:33
%S 273,54943,67303,199393,831283,1097305,1363723,1569103,1590433,
%T 3199579,3282433,3503773,5645563,5659333,9260053,9733843,9984115,
%U 10738033,16645363,19229533,32168743,37759363,38645233,50806585,53825497,56451373,58327423,62207173
%N Composite squarefree numbers n such that p-2 divides n+2 for each prime p dividing n.
%e 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.
%p with(numtheory); A225702:=proc(i,j) local c, d, n, ok, p, t;
%p for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
%p for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;
%p if not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;
%p if ok=1 then print(n); fi; fi; od; end: A225702(10^9,2);
%t 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
%o (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
%Y Cf. A208728, A225703-A225720.
%K nonn
%O 1,1
%A _Paolo P. Lava_, May 13 2013
%E Extended by _T. D. Noe_, May 17 2013
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