OFFSET
1,1
COMMENTS
Fixed points are the squarefree semiprimes.
EXAMPLE
For n=3 the minimum k is 195. Prime factors of 195 are 3, 5 and 13. We have: 195 - 3 = 192, 3 + 3 = 6 and 192 / 6 = 32, 5 + 3 = 8 and 192 / 8 = 24, 13 + 3 = 16 and 192 / 16 = 12.
MAPLE
with(numtheory); P:=proc(i) local c, d, k, n, ok, p; for k from 1 to i do
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 then ok:=0; break; fi;
if not type((n-k)/(p[d][1]+k), integer) then ok:=0; break; fi; od;
if ok=1 then print(n); break; fi; fi; od; od; end: P(10^6);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Aug 02 2013
STATUS
approved