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

1,1

Links

Table of n, a(n) for n=1..28.

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