A225715 Composite squarefree numbers n such that p(i)+5 divides n-5, where p(i) are the prime factors of n.

165, 1085, 3965, 4085, 5621, 7733, 8645, 14405, 19877, 23405, 33269, 40397, 45365, 66929, 88949, 110885, 114917, 135005, 243941, 275621, 280085, 421085, 439565, 455285, 460229, 474677, 480245, 496589, 505517, 518081, 570245, 706805, 709973, 900581, 912021

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..150

Example

Prime factors of 7733 are 11, 19 and 37. We have that (7733-5)/(11+5) = 483, (7733-5)/(19+5) = 322 and (7733-5)/(37+5) = 184.

Maple

with(numtheory); A225715:=proc(i, j) local c, d, n, ok, p, t;
for n from 2 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: A225715(10^9, -5);

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 - 5, p + 5]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

Crossrefs

Cf. A208728, A225702-A225714, A225716-A225720.

Sequence in context: A157090 A124409 A241614 * A066177 A184490 A027796

Adjacent sequences: A225712 A225713 A225714 * A225716 A225717 A225718

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Status

approved