A373414 Sum of the n-th maximal run of nonsquarefree numbers differing by one.

4, 17, 12, 16, 18, 20, 49, 55, 32, 36, 40, 89, 147, 52, 54, 56, 60, 127, 68, 72, 151, 161, 84, 88, 90, 92, 96, 297, 104, 108, 112, 233, 241, 375, 128, 132, 271, 140, 144, 295, 150, 305, 156, 160, 162, 164, 337, 343, 351, 180, 184, 377, 192, 196, 198, 200, 204

Offset

1,1

Comments

The length of this run is given by A053797.

A run of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by one.

Links

Table of n, a(n) for n=1..57.

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

Example

Row-sums of:
   4
   8   9
  12
  16
  18
  20
  24  25
  27  28
  32
  36
  40
  44  45
  48  49  50

Mathematica

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

Crossrefs

The partial sums are a subset of A329472.

Functional neighbors: A053797, A053806, A054265, A373406, A373412, A373413.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A049093, A049094, A061398, A061399, A077641, A077643, A101836, A143658 A294242, A373123, A373197.

Sequence in context: A264217 A341442 A063625 * A241257 A057596 A070712

Adjacent sequences: A373411 A373412 A373413 * A373415 A373416 A373417

Keyword

nonn

Author

Gus Wiseman, Jun 06 2024

Status

approved