A318841 a(n) = n - A173557(n).

0, 1, 1, 3, 1, 4, 1, 7, 7, 6, 1, 10, 1, 8, 7, 15, 1, 16, 1, 16, 9, 12, 1, 22, 21, 14, 25, 22, 1, 22, 1, 31, 13, 18, 11, 34, 1, 20, 15, 36, 1, 30, 1, 34, 37, 24, 1, 46, 43, 46, 19, 40, 1, 52, 15, 50, 21, 30, 1, 52, 1, 32, 51, 63, 17, 46, 1, 52, 25, 46, 1, 70, 1, 38, 67, 58, 17, 54, 1, 76, 79, 42, 1, 72, 21, 44, 31, 78, 1, 82, 19, 70, 33, 48

Offset: 1

Author

Antti Karttunen, Sep 16 2018

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A173557, A307868, A318833.

Programs

Mathematica

a[n_] := n - Times @@ (FactorInteger[n][[;;, 1]] - 1); a[1] = 0; Array[a, 100] (* Amiram Eldar, Dec 16 2023 *)

PARI

A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
A318841(n) = (n-A173557(n));

Formula

a(n) = n - A173557(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 - A307868 = 0.528319... . - Amiram Eldar, Dec 16 2023