A227976 - OEIS

%I #12 Jun 16 2016 21:53:52

%S 561,1595,35,6,21,6,15,14,21,10,35,22,33,14,15,133,65,34,51,38,21,22,

%T 95,46,69,26,115,217,161,30,87,62,33,34,35,1247,217,38,39,817,185,42,

%U 123,86,129,46,215,94,141,1247,51,1802,329,106,55,1541,57,58,371

%N 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.

%H Paolo P. Lava, <a href="/A227976/b227976.txt">Table of n, a(n) for n = 1..200</a>

%e For n=2 the minimum k is 1595. Prime factors of 1595 are 5, 11, and 29. We have 1595 - 2 = 1593, 5 - 2 = 2 and 1593 / 3 = 531, 11 - 2 = 9 and 1593 / 9 = 177, 29 - 2 = 27 and 1593 / 27 = 59.

%p with(numtheory); P:=proc(i) local c, d, k, n, ok, p; for k from 1 to i do

%p for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;

%p for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=k then ok:=0; break; fi;

%p if  not type((n-k)/(p[d][1]-k), integer) then ok:=0; break; fi; od;

%p if ok=1 then print(n); break; fi; fi; od; od; end: P(10^6);

%Y Cf. A208728, A225702-A225720, A227973-A227974.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Aug 06 2013