A070236 a(n) = Sum_{k=1..n} (core(k) - phi(k)), where core(k) is the squarefree part of k.

0, 1, 2, 1, 2, 6, 7, 5, 0, 6, 7, 6, 7, 15, 22, 15, 16, 12, 13, 10, 19, 31, 32, 30, 11, 25, 10, 5, 6, 28, 29, 15, 28, 46, 57, 46, 47, 67, 82, 76, 77, 107, 108, 99, 80, 104, 105, 92, 51, 33, 52, 41, 42, 30, 45, 35, 56, 86, 87, 86, 87, 119, 90, 59, 76, 122, 123, 108, 133, 179, 180

Offset: 1

Author

Benoit Cloitre, May 08 2002

Keywords

• easy
• nonn

Comments

a(n) is always >= 0.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Squarefree Part.
• Eric Weisstein's World of Mathematics, Totient Function.

Crossrefs

Cf. A000010, A002088, A007913, A069891.

Programs

Mathematica

f[n_] := Times @@ (First[#]^Mod[Last[#], 2] & /@ FactorInteger[n]) - EulerPhi[n]; Accumulate @ Array[f, 100] (* Amiram Eldar, Sep 06 2020 *)

PARI

for(n=1,100,print1(sum(i=1,n,core(i)-eulerphi(i)),","))

Formula

a(n) = A069891(n) - A002088(n) = Sum_{k=1..n} (A007913(k) - A000010(k)).

Asymptotically: a(n) = (Pi^2/30 - 3/Pi^2)*n^2 + O(n*log(n)).

Extensions

Various sections edited by Petros Hadjicostas, May 11 2020