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

1,2

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.

Links

Table of n, a(n) for n=1..58.

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

Mathematica

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

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.

Sequence in context: A019243 A375737 A246009 * A100871 A111860 A278160

Adjacent sequences: A373408 A373409 A373410 * A373412 A373413 A373414

Keyword

nonn

Author

Gus Wiseman, Jun 05 2024

Status

approved