A351827 - OEIS

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..60.

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

Adjacent sequences: A351824 A351825 A351826 * A351828 A351829 A351830

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Feb 20 2022

STATUS

approved