A227973 - OEIS

%I #7 Aug 06 2013 14:40:37

%S 15,273,77,6,21,6,33,10,15,14,21,33,35,22,33,26,39,57,65,34,51,38,57,

%T 551,95,46,69,203,115,145,161,58,87,62,93,629,155,697,217,74,111,518,

%U 185,82,123,86,129,2537,215,94,141,689,235,4366,329,106,159,1247,265

%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="/A227973/b227973.txt">Table of n, a(n) for n = 1..500</a>

%e For n=185 the minimum k is 543. Prime factors of 543 are 3 and 181. We have: 543 + 185 = 728, 3 - 185 = -182 and 728 / (-182) = -4, 181 - 185 = -4 and 728 / (-4) = 182.

%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, A227974-A227976.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Aug 02 2013