A225705 Composite squarefree numbers n such that p(i)-5 divides n+5, where p(i) are the prime factors of n.

21, 91, 187, 391, 3451, 4147, 6391, 7579, 8827, 9499, 9823, 11803, 15283, 21307, 22243, 26887, 29563, 36091, 42763, 49387, 62491, 63427, 84091, 89947, 107707, 116083, 126451, 139867, 155227, 227263, 270391, 287419, 302731, 317191, 320827, 376987, 381667, 433939

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..100

Example

Prime factors of 6391 are 7, 11 and 83. We have that (6391+5)/(7-5)  =3198, (6391+5)/(11-5) = 1066 and (6391+5)/(83-5) = 82.

Maple

with(numtheory); A225705:=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: A225705(10^9, 5);

Mathematica

t = {}; n = 0; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 5] > 0 && Union[Mod[n + 5, p - 5]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

Crossrefs

Cf. A208728, A225702-A225704, A225706-A225720.

Sequence in context: A223363 A284440 A020248 * A259758 A353056 A203173

Adjacent sequences: A225702 A225703 A225704 * A225706 A225707 A225708

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Status

approved