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 A345273 a(n) = Sum_{d|n} (n-d)^tau(d). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS If p is prime, a(p) = Sum_{d|p} (p-d)^tau(d) = (p-1)^1 + 0^2 = p-1. LINKS EXAMPLE a(10) = Sum_{d|10} (10-d)^tau(d) = 9^1 + 8^2 + 5^2 + 0^4 = 9 + 64 + 25 = 98. MATHEMATICA Table[Sum[(n - k)^DivisorSigma[0, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}] CROSSREFS Cf. A000005 (tau), A174937. Sequence in context: A190716 A303384 A013623 * A348145 A210421 A326098 Adjacent sequences:  A345270 A345271 A345272 * A345274 A345275 A345276 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jun 12 2021 STATUS approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)