A227974 Minimum composite squarefree numbers k such that p(i)+n divides k-n, for n=1, 2, 3, 4,..., where p(i) are the prime factors of k .

385, 182, 195, 1054, 165, 6, 1015, 4958, 2193, 10, 5159, 113937, 5593, 14, 15, 196009, 3657, 6318638, 2755, 1227818, 21, 22, 2795, 152358, 12121, 26, 21827, 17578, 36569, 30, 38335, 457907, 33, 34, 35

Offset: 1

Author

Paolo P. Lava, Aug 02 2013

Keywords

• nonn

Comments

Fixed points are the squarefree semiprimes.

Examples

			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.
		

Crossrefs

Cf. A208728, A225702-A225720, A227973, A227976.

Programs

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);