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

Offset: 1

Author

Reinhard Zumkeller, Mar 30 2007

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A007947, A033150, A051903, A128651.

Programs

Mathematica

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

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