A373411 Sum of the n-th maximal antirun of squarefree numbers differing by more than one.

1, 2, 8, 6, 17, 24, 14, 72, 22, 78, 30, 64, 34, 72, 38, 80, 42, 89, 263, 58, 120, 127, 66, 136, 70, 144, 151, 78, 161, 168, 86, 360, 94, 293, 102, 208, 106, 216, 110, 224, 114, 233, 241, 379, 130, 264, 271, 138, 280, 142, 288, 600, 312, 158, 648, 166, 510, 351

Offset: 1

Author

Gus Wiseman, Jun 05 2024

Keywords

• nonn

Comments

The length of this antirun is given by A373127.

An antirun of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by more than one.

Examples

			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
		

Links

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

Crossrefs

The partial sums are a subset of A173143.

Functional neighbors: A007674, A373127 (firsts A373128, sorted firsts A373200), A373404, A373405, A373408, A373412, A373413.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A025157, A049093, A061398, A077641, A077643, A112925, A112926, A143658, A372683, A373123, A373197, A373198.

Programs

Mathematica

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