A371191 Nonsquare terms of A349062.

1372, 465125, 4879688, 6272006419, 3533294646441, 405211279147678088

Offset: 1

Author

Amiram Eldar, Mar 14 2024

Keywords

• nonn
• hard
• more

Comments

There are no more terms below 10^18.

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

Examples

			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.
		

Links

• Index entries for sequences related to powerful numbers.

Crossrefs

Intersection of A000037 and A349062.

Cf. A227297.

Programs

Mathematica

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]

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], ", "))));}