A066503 a(n) = n - squarefree kernel of n, A007947.

0, 0, 0, 2, 0, 0, 0, 6, 6, 0, 0, 6, 0, 0, 0, 14, 0, 12, 0, 10, 0, 0, 0, 18, 20, 0, 24, 14, 0, 0, 0, 30, 0, 0, 0, 30, 0, 0, 0, 30, 0, 0, 0, 22, 30, 0, 0, 42, 42, 40, 0, 26, 0, 48, 0, 42, 0, 0, 0, 30, 0, 0, 42, 62, 0, 0, 0, 34, 0, 0, 0, 66, 0, 0, 60, 38, 0, 0

Offset: 1

Author

Reinhard Zumkeller, Jan 04 2002

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005117, A007947, A065463.

Programs

Mathematica

a[n_] := n - Times @@ FactorInteger[n][[All, 1]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Dec 01 2021 *)

PARI

{ for (n=1, 1000, f=factor(n); k=1; for(i=1, matsize(f)[1], k*=f[i, 1]); write("b066503.txt", n, " ", n - k) ) } \\ Harry J. Smith, Feb 18 2010

Formula

a(n) = n - A007947(n).

a(A005117(n)) = 0.

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 - A065463 = 0.295557... . - Amiram Eldar, Dec 05 2023