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

Author

Paolo P. Lava, May 13 2013

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A208728, A225702-A225718, A225720.

Programs

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);