A371191 - OEIS

%I #5 Mar 14 2024 11:09:32

%S 1372,465125,4879688,6272006419,3533294646441,405211279147678088

%N Nonsquare terms of A349062.

%C There are no more terms below 10^18.

%C There are 276407671 terms of A349062 below 10^18, of them only 6 are nonsquare numbers.

%H <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.

%e 1372 = 2^2 * 7^3 is a term since it is a term of A349062 (the gap to the next powerful number, 1444, is 72, which is a record) and it is not a square.

%t seq[max_] := Module[{pows = Union[Flatten[Table[i^2*j^3, {j, 1, Surd[max, 3]}, {i, 1, Sqrt[max/j^3]}]]], gapmax = 0, gap, s = {}}, Do[gap = pows[[k+1]] - pows[[k]]; If[gap > gapmax, gapmax = gap; If[!IntegerQ[Sqrt[pows[[k]]]], AppendTo[s, pows[[k]]]]], {k, 1, Length[pows] - 1}]; s]; seq[10^10]

%o (PARI) lista(mx) = {my(s = List(), gap, gapmax = 0); for(j = 1, sqrtnint(mx, 3), for(i = 1, sqrtint(mx\j^3), listput(s, i^2 * j^3))); s = Set(s); for(k = 1, #s - 1, gap = s[k+1] - s[k]; if(gap > gapmax, gapmax = gap; if(!issquare(s[k]), print1(s[k], ", "))));}

%Y Intersection of A000037 and A349062.

%Y Cf. A227297.

%K nonn,hard,more

%O 1,1

%A _Amiram Eldar_, Mar 14 2024