A373123 Sum of all squarefree numbers from 2^(n-1) to 2^n - 1.

1, 5, 18, 63, 218, 891, 3676, 15137, 60580, 238672, 953501, 3826167, 15308186, 61204878, 244709252, 979285522, 3917052950, 15664274802, 62663847447, 250662444349, 1002632090376, 4010544455838, 16042042419476, 64168305037147, 256675237863576

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Example

This is the sequence of row sums of A005117 treated as a triangle with row-lengths A077643:
   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  58  59  61  62

Mathematica

Table[Total[Select[Range[2^(n-1), 2^n-1], SquareFreeQ]], {n, 10}]

Prog

(PARI) a(n) = my(s=0); forsquarefree(i=2^(n-1), 2^n-1, s+=i[1]); s; \\ Michel Marcus, May 29 2024

Crossrefs

Counting all numbers (not just squarefree) gives A010036.

For the sectioning of A005117:

Row-lengths are A077643, partial sums A143658.

First column is A372683, delta A373125, indices A372540, firsts of A372475.

Last column is A372889, delta A373126, indices A143658, diffs A077643.

For primes instead of powers of two:

- sum A373197

- length A373198 = A061398 - 1

- maxima A112925, opposite A112926

For prime instead of squarefree:

- sum A293697 (except initial terms)

- length A036378

- min A104080 or A014210, indices A372684 (firsts of A035100)

- max A014234, delta A013603

A000120 counts ones in binary expansion (binary weight), zeros A080791.

A005117 lists squarefree numbers, first differences A076259.

A030190 gives binary expansion, reversed A030308.

A070939 or (preferably) A029837 gives length of binary expansion.

Cf. A372473 (firsts of A372472), A372541 (firsts of A372433).

Cf. A029931, A048793, A049093, A049094, A059015, A069010, A077641.

Sequence in context: A372420 A121050 A029869 * A033453 A284840 A301749

Adjacent sequences: A373120 A373121 A373122 * A373124 A373125 A373126

Keyword

nonn

Author

Gus Wiseman, May 27 2024

Status

approved