A225710 Composite squarefree numbers n such that p(i)-10 divides n+10, where p(i) are the prime factors of n.

14, 22, 35, 55, 65, 77, 102, 110, 143, 165, 182, 221, 455, 494, 665, 935, 1001, 1173, 1430, 2717, 2795, 4505, 4526, 4862, 5957, 6479, 11526, 27521, 30485, 34661, 35126, 45917, 49715, 52910, 53846, 81686, 90574, 106865, 113477, 118745, 139073, 140822, 147095

Offset: 1

Author

Paolo P. Lava, May 13 2013

Keywords

• nonn

Examples

			Prime factors of 34661 are 11, 23 and 137. We have that (34661+10)/(11-10) = 34671, (34661+10)/(23-10) = 2667 and (34661+10)/(137-10) = 273.
		

Crossrefs

Cf. A208728, A225702-A225709, A225711-A225720.

Programs

Maple

with(numtheory); A225710:=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: A225710(10^9,10);

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 + 10, p - 10]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

Extensions

Extended by T. D. Noe, May 17 2013