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A227973 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.

%I A227973 #7 Aug 06 2013 14:40:37
%S A227973 15,273,77,6,21,6,33,10,15,14,21,33,35,22,33,26,39,57,65,34,51,38,57,
%T A227973 551,95,46,69,203,115,145,161,58,87,62,93,629,155,697,217,74,111,518,
%U A227973 185,82,123,86,129,2537,215,94,141,689,235,4366,329,106,159,1247,265
%N A227973 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 A227973 Paolo P. Lava, <a href="/A227973/b227973.txt">Table of n, a(n) for n = 1..500</a>
%e A227973 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 A227973 with(numtheory); P:=proc(i) local c, d, k, n, ok, p; for k from 1 to i do
%p A227973 for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
%p A227973 for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=k then ok:=0; break; fi;
%p A227973 if  not type((n+k)/(p[d][1]-k), integer) then ok:=0; break; fi; od;
%p A227973 if ok=1 then print(n); break; fi; fi; od; od; end: P(10^6);
%Y A227973 Cf. A208728, A225702-A225720, A227974-A227976.
%K A227973 nonn
%O A227973 1,1
%A A227973 _Paolo P. Lava_, Aug 02 2013