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A344308 Numbers k such that A205791(k) = k+1.

%I A344308 #15 May 19 2021 02:13:56
%S A344308 1,2,3,5,6,7,10,13,14,15,17,19,21,23,26,29,30,34,35,37,38,39,42,43,46,
%T A344308 47,51,53,57,58,59,65,67,69,70,73,74,78,79,83,85,86,87,89,91,94,95,97,
%U A344308 102,103,105,106,107,109,111,113,114,115,118,119,127,129,130,133,134,137,138,139,141,145
%N A344308 Numbers k such that A205791(k) = k+1.
%H A344308 Robert Israel, <a href="/A344308/b344308.txt">Table of n, a(n) for n = 1..1258</a>
%e A344308 a(6) = 7 is a term because A205791(7) = 8.
%p A344308 N:= 200: # for terms <= N
%p A344308 V:= Vector(N):
%p A344308 count:= 0:
%p A344308 for k from 1 while count < N do
%p A344308   for j from 1 to k-1 while count < N do
%p A344308     Q:= select(t -> t <= N and V[t] = 0, numtheory:-divisors(k^5-j^5));
%p A344308     if Q <> {} then
%p A344308        newcount:= nops(Q);
%p A344308        count:= count + newcount;
%p A344308        V[convert(Q, list)]:= k;
%p A344308     fi
%p A344308 od od:
%p A344308 select(t -> V[t] = t+1, [$1..N]);
%t A344308 Select[Range@200,(k=1;While[FreeQ[Mod[Table[k^5-j^5,{j,k-1}],#],0],k++];k)==#+1&] (* _Giorgos Kalogeropoulos_, May 14 2021 *)
%Y A344308 Cf. A205791.
%Y A344308 Subset of A005117.
%K A344308 nonn
%O A344308 1,2
%A A344308 _Robert Israel_, May 14 2021