A225704 Composite squarefree numbers n such that p(i)-4 divides n+4, where p(i) are the prime factors of n.

6, 10, 14, 15, 30, 35, 66, 266, 455, 806, 4154, 4686, 6665, 10370, 16646, 22781, 31146, 36305, 72086, 205871, 246506, 473711, 570011, 653666, 733586, 900581, 904046, 1422410, 1941971, 1969565, 2023010, 2807255, 2821269, 3009821, 3043274, 3355271, 3880301

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Example

Prime factors of 205871 are 29, 31 and 229. We have that (205871+4)/(29-4) = 8235, (205871+4)/(31-4) = 7625 and (205871+4)/(229-4) = 915.

Maple

with(numtheory); A225704:=proc(i, j) local c, d, n, ok, p, t;
for n from 1 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: A225704(10^9, 4);

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 + 4, p - 4]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

Crossrefs

Cf. A208728, A225702, A225703, A225705-A225720.

Sequence in context: A226494 A242920 A183072 * A228301 A193416 A338703

Adjacent sequences: A225701 A225702 A225703 * A225705 A225706 A225707

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Extensions

Extended by T. D. Noe, May 17 2013

Status

approved