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A354112
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Total number of 1's in binary expansion of all divisors of 2^n-1.
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1
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1, 3, 4, 9, 6, 17, 8, 27, 16, 33, 20, 100, 14, 44, 42, 81, 18, 186, 20, 293, 80, 118, 38, 634, 62, 77, 64, 523, 80, 813, 32, 243, 153, 99, 154, 5031, 58, 110, 189, 1918, 67, 1624, 115, 1545, 761, 226, 120, 9366, 64, 1728, 472, 1861, 135, 2162, 945, 3471, 261, 1056, 101, 73418
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OFFSET
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1,2
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LINKS
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FORMULA
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MAPLE
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a:= n-> add(add(i, i=Bits[Split](d)), d=numtheory[divisors](2^n-1)):
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MATHEMATICA
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a[n_] := Total[DigitCount[Divisors[2^n - 1], 2, 1]]; Array[a, 60] (* Amiram Eldar, May 17 2022 *)
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PROG
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(PARI) a(n) = sumdiv(2^n-1, d, hammingweight(d));
(Python 3.10+)
# if python version < 3.10, replace d.bitcount() with bin(d).count('1')
from sympy import divisors
def A354112(n): return sum(d.bit_count() for d in divisors(2**n-1, generator=True)) # Chai Wah Wu, May 17 2022
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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