A375705 Sum of the n-th maximal run of adjacent (increasing by one at a time) non-perfect-powers.

5, 18, 75, 164, 26, 118, 102, 510, 791, 1160, 1629, 2210, 369, 253, 2040, 3756, 4745, 3914, 1764, 3978, 2994, 8720, 10421, 6003, 5984, 14459, 16820, 19425, 13446, 8328, 25415, 28824, 32525, 36530, 40851, 45500, 50489, 55830, 37259, 23276, 67616, 74085, 80954

Offset: 1

Author

Gus Wiseman, Aug 29 2024

Keywords

• nonn

Comments

Non-perfect-powers (A007916) are numbers without a proper integer root.

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 begins with A375703(n), ends with A375704(n), adds up to a(n), and has length A375702(n).
		

Crossrefs

For nonprime numbers we have A054265, anti-runs A373404.

For nonsquarefree numbers we have A373414, anti-runs A373412.

For squarefree numbers we have A373413, anti-runs A373411.

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

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

The anti-run version is A375737, sums of A375736.

A001597 lists perfect-powers, differences A053289.

A007916 lists non-perfect-powers, differences A375706.

A046933 counts composite numbers between primes.

For runs of non-perfect-powers:

- length: A375702 = A053289(n+1) - 1

- first: A375703 (same as A216765 with 2 exceptions)

- last: A375704 (same as A045542 with 8 removed)

- sum: A375705 (this)

Cf. A006093, A006549, A251092, A255346, A371201, A373197, A375708.

Programs

Mathematica

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