A375702 Length of the n-th maximal run of adjacent (increasing by one at a time) non-perfect-powers.

2, 3, 6, 8, 1, 4, 3, 12, 14, 16, 18, 20, 3, 2, 15, 24, 26, 19, 8, 17, 12, 32, 34, 18, 17, 38, 40, 42, 27, 16, 46, 48, 50, 52, 54, 56, 58, 60, 38, 23, 64, 66, 68, 70, 34, 37, 74, 76, 78, 80, 46, 35, 84, 86, 88, 22, 67, 70, 9, 11, 94, 96, 98, 100, 102, 39, 64

Offset: 1

Author

Gus Wiseman, Aug 27 2024

Keywords

• nonn

Comments

Non-perfect-powers A007916 are numbers with no proper integer roots.

Examples

			The list of all non-perfect-powers, split into runs, begins:
   2   3
   5   6   7
  10  11  12  13  14  15
  17  18  19  20  21  22  23  24
  26
  28  29  30  31
  33  34  35
  37  38  39  40  41  42  43  44  45  46  47  48
Row n has length a(n), first A375703, last A375704, sum A375705.
		

Crossrefs

For nonsquarefree numbers we have A053797, anti-runs A373409.

For squarefree numbers we have A120992, anti-runs A373127.

For nonprime numbers we have A176246, anti-runs A373403.

For prime-powers we have A373675, anti-runs A373576.

For non-prime-powers we have A373678, anti-runs A373679.

The anti-run version is A375736, sum A375737.

For runs of non-perfect-powers (A007916):

- length: A375702 (this).

- first: A375703

- last: A375704

- sum: A375705

A001597 lists perfect-powers, differences A053289.

A007916 lists non-perfect-powers, differences A375706.

A046933 counts composite numbers between primes.

Cf. A007674, A045542, A061399, A216765, A251092, A375708, A375714.

Programs

Mathematica

radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
Length/@Split[Select[Range[100],radQ],#1+1==#2&]//Most

Formula

For n > 2 we have a(n) = A053289(n+1) - 1.