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A070236 a(n) = Sum_{k=1..n} (core(k) - phi(k)), where core(k) is the squarefree part of k. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)