A225708 Composite squarefree numbers n such that p(i)-8 divides n+8, where p(i) are the prime factors of n.

10, 22, 55, 70, 154, 190, 322, 385, 442, 595, 682, 2002, 2737, 3619, 5530, 14986, 23782, 24817, 25102, 26767, 30430, 31042, 34762, 37810, 85462, 106582, 141427, 171790, 189727, 225910, 243217, 248482, 255142, 272782, 307090, 381547, 388102, 471262, 637849, 798490

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Example

Prime factors of 381547 are 23, 53 and 313. We have that (381547+8)/(23-8)=25437, (381547+8)/(53-8)=8479 and (381547+8)/(313-8)=1251.

Maple

with(numtheory); A225708:=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: A225708(10^9, 8);

Mathematica

t = {}; n = 0; While[Length[t] < 40, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n + 8, p - 8]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

Crossrefs

Cf. A208728, A225702-A225707, A225709-A225720.

Sequence in context: A219744 A246419 A039315 * A088871 A043138 A043918

Adjacent sequences: A225705 A225706 A225707 * A225709 A225710 A225711

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Status

approved