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

Author

Gus Wiseman, Jun 06 2024

Keywords

• nonn

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.

Examples

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

Links

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

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.

Programs

Mathematica

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