A351827 Sum of the numbers <= n that are either prime, a divisor of n, or both.
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
Offset: 1
Keywords
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