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A356100
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a(n) = Sum_{k=1..n} (k - 1)^n * floor(n/k).
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2
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0, 1, 9, 99, 1301, 20581, 376891, 7914216, 186905206, 4915451602, 142368695176, 4506118905870, 154720069309364, 5729167232515112, 227585086051159866, 9654819212943764500, 435659280972794395356, 20836049921760968809231, 1052864549462731148832219
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} Sum_{d|k} (d - 1)^n.
a(n) = [x^n] (1/(1-x)) * Sum_{k>=1} (k - 1)^n * x^k/(1 - x^k).
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PROG
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(PARI) a(n) = sum(k=1, n, (k-1)^n*(n\k));
(PARI) a(n) = sum(k=1, n, sigma(k, n)-(n\k)^n);
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, (d-1)^n));
(Python)
def A356100(n): return sum((k-1)**n*(n//k) for k in range(2, n+1)) # Chai Wah Wu, Jul 26 2022
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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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