A373412 Sum of the n-th maximal antirun of nonsquarefree numbers differing by more than one.

12, 99, 52, 180, 93, 49, 335, 279, 156, 629, 99, 540, 237, 245, 125, 521, 567, 450, 963, 340, 347, 728, 1386, 1080, 1637, 243, 244, 1511, 1610, 555, 852, 1171, 2142, 960, 985, 1689, 343, 1042, 351, 1068, 724, 732, 1116, 1905, 1980, 2898, 424, 2161, 3150, 2339

Offset

1,1

Comments

The length of this antirun is given by A373409.

An antirun of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by more than one.

Links

Table of n, a(n) for n=1..50.

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  52  54  56  60  63
  64  68  72  75
  76  80
  81  84  88  90  92  96  98
  99

Mathematica

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

Crossrefs

The partial sums are a subset of A329472.

Functional neighbors: A068781, A373404, A373405, A373409, A373410, A373411, A373414.

A005117 lists the squarefree numbers, first differences A076259.

A013929 lists the nonsquarefree numbers, first differences A078147.

Cf. A025157, A049093, A049094, A061399, A101836, A112925, A143658, A294242, A350842, A372683, A373197.

Sequence in context: A216028 A238755 A159449 * A282285 A090230 A133652

Adjacent sequences: A373409 A373410 A373411 * A373413 A373414 A373415

Keyword

nonn

Author

Gus Wiseman, Jun 06 2024

Status

approved