A225702 Composite squarefree numbers n such that p-2 divides n+2 for each prime p dividing n.

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

Offset: 1

Author

Paolo P. Lava, May 13 2013

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A208728, A225703-A225720.

Programs

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

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

Extensions

Extended by T. D. Noe, May 17 2013