A345001 - OEIS

A345001

a(n) = sigma(n) + n' - 2n, where n' is the arithmetic derivative of n (A003415) and sigma is the sum of divisors (A000203).

-1, 0, -1, 3, -3, 5, -5, 11, 1, 5, -9, 20, -11, 5, 2, 31, -15, 24, -17, 26, 0, 5, -21, 56, -9, 5, 13, 32, -27, 43, -29, 79, -4, 5, -10, 79, -35, 5, -6, 78, -39, 53, -41, 44, 27, 5, -45, 140, -27, 38, -10, 50, -51, 93, -22, 100, -12, 5, -57, 140, -59, 5, 29, 191, -28, 73, -65, 62, -16, 63, -69, 207, -71, 5, 29, 68

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OFFSET

1,4

COMMENTS

Coincides with A003415 only on perfect numbers (A000396).

LINKS

Table of n, a(n) for n=1..76.

FORMULA

a(n) = A003415(n) - A033879(n) = A000203(n) + A003415(n) - 2*n.

a(n) = A001065(n) + A168036(n).

a(n) = A344999(n) / A048250(n) = A345049(n) / A173557(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A013661 + A136141 - 2 = 0.418090735898... . - Amiram Eldar, Dec 08 2023