A225719 Composite squarefree numbers n such that p(i)+9 divides n-9, where p(i) are the prime factors of n.

2193, 3705, 9889, 12749, 23529, 116265, 283929, 514569, 641769, 661789, 772809, 950609, 1144313, 1241561, 1452009, 1708233, 1797609, 1878569, 2244901, 2255689, 2675409, 2792937, 3426089, 4021369, 4187465, 5242569, 7327329, 7942209, 8601329, 8668921, 9608729

Offset

1,1

Links

Table of n, a(n) for n=1..31.

Example

Prime factors of 116265 are 3, 5, 23 and 337. We have that (116265-9)/(3+9) = 9688, (116265-9)/(5+9) = 8304, (116265-9)/(23+9) = 3633 and (116265-9)/(337+9) = 336.

Maple

with(numtheory); A225719:=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: A225719(10^9, -9);

Crossrefs

Cf. A208728, A225702-A225718, A225720.

Sequence in context: A320718 A134158 A227488 * A352344 A342428 A229319

Adjacent sequences: A225716 A225717 A225718 * A225720 A225721 A225722

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Status

approved