A373413 Sum of the n-th maximal run of squarefree numbers.

6, 18, 21, 42, 17, 19, 66, 26, 90, 102, 114, 126, 93, 51, 53, 55, 174, 123, 198, 210, 147, 234, 165, 258, 89, 91, 282, 97, 306, 318, 330, 342, 237, 245, 127, 390, 267, 414, 426, 291, 149, 151, 309, 474, 161, 163, 498, 170, 347, 534, 546, 558, 381, 582, 197

Offset

1,1

Comments

The length of this run is given by A120992.

A run of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by one.

Links

Table of n, a(n) for n=1..55.

Gus Wiseman, Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers

Example

Row-sums of:
   1   2   3
   5   6   7
  10  11
  13  14  15
  17
  19
  21  22  23
  26
  29  30  31
  33  34  35
  37  38  39
  41  42  43
  46  47
  51
  53
  55
  57  58  59

Mathematica

Total/@Split[Select[Range[100], SquareFreeQ], #1+1==#2&]//Most

Crossrefs

The partial sums are a subset of A173143.

Functional neighbors: A054265, A072284, A120992, A373406, A373411, A373414, A373415.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A049093, A049095, A061398, A077641, A077643, A143658, A371201, A373123, A373125, A373126, A373197.

Sequence in context: A186889 A022418 A350848 * A358748 A081318 A275168

Adjacent sequences: A373410 A373411 A373412 * A373414 A373415 A373416

Keyword

nonn

Author

Gus Wiseman, Jun 05 2024

Status

approved