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A225702
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Composite squarefree numbers n such that p-2 divides n+2 for each prime p dividing n.
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33
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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