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

1,1

Links

Table of n, a(n) for n=1..30.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A023904 A035839 A048546 * A371805 A015306 A190830

Adjacent sequences: A225709 A225710 A225711 * A225713 A225714 A225715

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Status

approved