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

Author

Paolo P. Lava, May 13 2013

Keywords

• nonn

Examples

			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.
		

Crossrefs

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

Programs

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 *)