A129132 - OEIS

A129132

Partial sums of A051903.

0, 1, 2, 4, 5, 6, 7, 10, 12, 13, 14, 16, 17, 18, 19, 23, 24, 26, 27, 29, 30, 31, 32, 35, 37, 38, 41, 43, 44, 45, 46, 51, 52, 53, 54, 56, 57, 58, 59, 62, 63, 64, 65, 67, 69, 70, 71, 75, 77, 79, 80, 82, 83, 86, 87, 90, 91, 92, 93, 95, 96, 97, 99, 105, 106, 107, 108, 110, 111, 112

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n+1) = a(n) + A051903(n), a(1) = 0;

A128651(a(n-1) + 2) = A007947(n) for n>1.

a(n) ~ c * n, where c is Niven's constant (A033150). - Amiram Eldar, Oct 19 2020

a(n) = - Sum_{i=2..n} Sum_{j=1..n} mobius(i)*floor(n/(i^j)). - Ridouane Oudra, Nov 22 2024

MATHEMATICA

f[1] = 0; f[n_] := Max @ FactorInteger[n][[;; , 2]]; Accumulate @ Array[f, 70] (* Amiram Eldar, Oct 19 2020 *)