login
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
OFFSET
1,3
COMMENTS
a(n) is always >= 0.
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 08 2002
EXTENSIONS
Various sections edited by Petros Hadjicostas, May 11 2020
STATUS
approved