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A351827 Sum of the numbers <= n that are either prime, a divisor of n, or both. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
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
CROSSREFS
Cf. A000203 (sigma), A008472 (sopf), A010051, A034387, A351519.
Sequence in context: A105359 A105355 A183545 * A351828 A158975 A282876
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Feb 20 2022
STATUS
approved

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Last modified July 13 11:10 EDT 2024. Contains 374282 sequences. (Running on oeis4.)