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A345273
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a(n) = Sum_{d|n} (n-d)^tau(d).
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0
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0, 1, 2, 7, 4, 30, 6, 107, 44, 98, 10, 2000, 12, 206, 258, 6035, 16, 21963, 18, 14664, 540, 542, 22, 3165444, 424, 770, 6434, 53384, 28, 544568, 30, 1403235, 1416, 1346, 1718, 225979931, 36, 1694, 2010, 65907940, 40, 2493140, 42, 301152, 860064, 2510, 46, 112291412012, 1812
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OFFSET
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1,3
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COMMENTS
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If p is prime, a(p) = Sum_{d|p} (p-d)^tau(d) = (p-1)^1 + 0^2 = p-1.
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LINKS
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EXAMPLE
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a(10) = Sum_{d|10} (10-d)^tau(d) = 9^1 + 8^2 + 5^2 + 0^4 = 9 + 64 + 25 = 98.
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MATHEMATICA
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Table[Sum[(n - k)^DivisorSigma[0, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]
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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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