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A351827
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Sum of the numbers <= n that are either prime, a divisor of n, or both.
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0
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1, 3, 6, 10, 11, 17, 18, 30, 27, 28, 29, 51, 42, 56, 57, 70, 59, 92, 78, 112, 99, 100, 101, 155, 126, 127, 137, 147, 130, 191, 161, 221, 194, 195, 196, 246, 198, 236, 237, 280, 239, 322, 282, 352, 351, 328, 329, 447, 378, 414, 380, 411, 382, 496, 437, 492, 439, 440, 441, 598
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} k * (u(k) + v(n/k) - u(k)*v(n/k)), where u(n) is the prime characteristic (A010051) and v(n) = 1 - ceiling(n) + floor(n).
a(n) = sigma(n) - sopf(n) + Sum_{p<=n, p prime} p. - Wesley Ivan Hurt, Dec 31 2023
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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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