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

1,3

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.

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)).

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A002088, A007913, A069891.

Sequence in context: A153896 A074727 A059587 * A020825 A259992 A110422

Adjacent sequences: A070233 A070234 A070235 * A070237 A070238 A070239

Keyword

easy,nonn

Author

Benoit Cloitre, May 08 2002

Extensions

Various sections edited by Petros Hadjicostas, May 11 2020

Status

approved