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A373123
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Sum of all squarefree numbers from 2^(n-1) to 2^n - 1.
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11
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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Table[Total[Select[Range[2^(n-1), 2^n-1], SquareFreeQ]], {n, 10}]
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PROG
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(PARI) a(n) = my(s=0); forsquarefree(i=2^(n-1), 2^n-1, s+=i[1]); s; \\ Michel Marcus, May 29 2024
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CROSSREFS
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Counting all numbers (not just squarefree) gives A010036.
For primes instead of powers of two:
For prime instead of squarefree:
- sum A293697 (except initial terms)
A000120 counts ones in binary expansion (binary weight), zeros A080791.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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