A373197 Sum of all squarefree numbers from prime(n) to prime(n+1) - 1.

2, 3, 11, 17, 11, 42, 17, 62, 49, 59, 133, 114, 83, 89, 98, 223, 59, 254, 206, 71, 302, 161, 341, 462, 97, 203, 314, 107, 330, 824, 386, 398, 275, 856, 149, 460, 635, 494, 337, 702, 179, 1294, 191, 582, 197, 1635, 1950, 449, 227, 690, 943, 239, 983, 1013, 1036

Offset: 1

Author

Gus Wiseman, May 29 2024

Keywords

• nonn

Examples

			This is the sequence of row sums of A005117 treated as a triangle with row-lengths A373198:
   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
		

Crossrefs

Counting all numbers (not just squarefree) gives A371201.

For the sectioning of A005117 (squarefree between prime):

- sum is A373197 (this sequence)

- length is A373198 = A061398 - 1

- min is A000040

- max is A112925, opposite A112926

For squarefree numbers between powers of two:

- sum is A373123

- length is A077643, partial sums A143658

- min is A372683, delta A373125, indices A372540, firsts of A372475

- max is A372889, delta A373126

For primes between powers of two:

- sum is A293697 (except initial terms)

- length is A036378

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

- max is A014234, delta A013603

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

Cf. A046933, A049093, A049094, A076259, A077641.

Programs

Mathematica

Table[Total[Select[Range[Prime[n],Prime[n+1]-1],SquareFreeQ]],{n,15}]