A225712 Composite squarefree numbers n such that p(i)+2 divides n-2, where p(i) are the prime factors of n.

182, 21827, 32942, 46055, 84502, 151202, 191522, 361802, 532247, 780626, 1368642, 1398377, 1425230, 1556258, 1751927, 1932338, 2209727, 3496502, 4078802, 4216862, 4438709, 5191562, 5991477, 7413002, 8385365, 8797502, 11749127, 13634138, 15921677, 16772177

Offset: 1

Author

Paolo P. Lava, May 13 2013

Keywords

• nonn

Examples

			Prime factors of 151202 are 2, 19, 23 and 173. We have that (151202-2)/(2+2) = 37800, (151202-2)/(19+2) = 7200, (151202-2)/(23+2) = 6048 and (151202-2)/(173+2)= 864.
		

Crossrefs

Cf. A208728, A225702-A225711, A225713-A225720.

Programs

Maple

with(numtheory); A225712:=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: A225712(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} && Union[Mod[n - 2, p + 2]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)