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

1,1

Links

Table of n, a(n) for n=1..43.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A187776 A048196 A305084 * A183185 A324526 A259750

Adjacent sequences: A225707 A225708 A225709 * A225711 A225712 A225713

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Extensions

Extended by T. D. Noe, May 17 2013

Status

approved