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A085831
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a(n) = Sum_{k=1..2^n} d(k) where d(n) = number of divisors of n (A000005).
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6
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1, 3, 8, 20, 50, 119, 280, 645, 1466, 3280, 7262, 15937, 34720, 75108, 161552, 345785, 736974, 1564762, 3311206, 6985780, 14698342, 30850276, 64607782, 135030018, 281689074, 586636098, 1219788256, 2532608855, 5251282902, 10874696106, 22493653324, 46475828418
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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k = s = 0; Do[ While[ k < 2^n, k++; s = s + DivisorSigma[ 0, k ]]; Print[s], {n, 0, 29} ]
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PROG
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(Python)
from math import isqrt
def A085831(n): return (lambda m, r: 2*sum(r//k for k in range(1, m+1))-m*m)(isqrt(2**n), 2**n) # Chai Wah Wu, Oct 08 2021
(PARI) a(n) = sum(k=1, 2^n, numdiv(k)); \\ Michel Marcus, Oct 10 2021
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CROSSREFS
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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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