A371190 The smaller of a pair of successive powerful numbers without a nonsquarefree number between them.

1, 4, 8, 25, 32, 288, 675, 968, 1152, 1369, 2700, 9800, 12167, 39200, 48668, 70225, 235224, 332928, 465124, 1331712, 1825200, 5724500, 7300800, 11309768, 78960996, 189750625, 263672644, 384199200, 592192224, 912670088, 1536796800, 2368768896, 4931691075, 5425069447, 8957108164

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..64

Index entries for sequences related to powerful numbers.

Example

1 is a term since 1 and 4 are successive powerful numbers and the numbers between them, 2 and 3, are both squarefree.

Mathematica

seq[max_] := Module[{pows = Union[Flatten[Table[i^2*j^3, {j, 1, Surd[max, 3]}, {i, 1, Sqrt[max/j^3]}]]], s = {}}, Do[If[AllTrue[Range[pows[[k]] + 1, pows[[k + 1]] - 1], SquareFreeQ], AppendTo[s, pows[[k]]]], {k, 1, Length[pows] - 1}]; s]; seq[10^10]

Prog

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

Crossrefs

Cf. A001694, A005117, A013929, A240591.

Sequence in context: A131637 A163143 A154586 * A185615 A068367 A292548

Adjacent sequences: A371187 A371188 A371189 * A371191 A371192 A371193

Keyword

nonn

Author

Amiram Eldar, Mar 14 2024

Status

approved