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A363421
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a(n) = Sum_{k=0..n}(n^[not(k | n)] - n^[k | n]), where '[ ]' denotes the Iverson bracket.
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5
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1, 0, -1, 0, -3, 8, -5, 24, 7, 32, 27, 80, 11, 120, 91, 112, 105, 224, 119, 288, 171, 280, 315, 440, 207, 480, 475, 520, 459, 728, 435, 840, 651, 832, 891, 952, 665, 1224, 1147, 1216, 975, 1520, 1107, 1680, 1419, 1496, 1755, 2024, 1363, 2112, 1911, 2200, 2091
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = n^2 - 2*(n - 1)*tau(n) - 1 for n >= 1, where tau = A000005.
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MATHEMATICA
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PROG
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(SageMath)
print([sum(n^(not k.divides(n)) - n^k.divides(n) for k in srange(n+1)) for n in srange(53)])
(Python)
from sympy import divisor_count
def A363421(n): return n**2-2*(n-1)*divisor_count(n)-1 if n else 1 # Chai Wah Wu, Jun 28 2023
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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