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

1,4

Links

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

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A005117, A007947, A065463.

Sequence in context: A372361 A334045 A028973 * A057385 A231108 A231285

Adjacent sequences: A066500 A066501 A066502 * A066504 A066505 A066506

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jan 04 2002

Status

approved