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A265204 Sum of phi(i) over squarefree numbers i <= n. 1
1, 2, 4, 4, 8, 10, 16, 16, 16, 20, 30, 30, 42, 48, 56, 56, 72, 72, 90, 90, 102, 112, 134, 134, 134, 146, 146, 146, 174, 182, 212, 212, 232, 248, 272, 272, 308, 326, 350, 350, 390, 402, 444, 444, 444, 466, 512, 512, 512, 512, 544, 544, 596, 596, 636, 636, 672, 700, 758, 758, 818, 848, 848, 848, 896, 916, 982, 982, 1026, 1050 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial sums of absolute values of A097945. - Robert Israel, Dec 10 2015

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

with(numtheory):

a:= proc(n) option remember; `if`(n=0, 0, a(n-1))+

      `if`(issqrfree(n), phi(n), 0)

    end:

seq(a(n), n=1..70);  # Alois P. Heinz, Dec 04 2015

N:= 1000: # to get a(1) to a(N)

V:= Vector(N, 1):

Primes:= select(isprime, [2, seq(i, i=3..N, 2)]):

for p in Primes do

  J1:= [seq(i, i=p..N, p)];

  J2:= [seq(i, i=p^2..N, p^2)];

  V[J1]:= V[J1] * (p-1);

  V[J2]:= 0;

od:

ListTools[PartialSums](convert(V, list)); # Robert Israel, Dec 10 2015

MATHEMATICA

Table[Sum[EulerPhi@ i, {i, Select[Range@ n, SquareFreeQ]}], {n, 70}] (* Michael De Vlieger, Dec 10 2015 *)

PROG

(PARI) a(n) = sum(i=1, n, eulerphi(i)*issquarefree(i)) \\ Anders Hellström, Dec 04 2015

(Perl) use ntheory ":all"; sub an { vecsum(map { is_square_free($_) ? euler_phi($_) : () } 1..shift); } say an($_) for 1..70; # Dana Jacobsen, Dec 10 2015

CROSSREFS

Cf. A000010, A097945.

Sequence in context: A039879 A125204 A241386 * A073420 A034408 A227333

Adjacent sequences:  A265201 A265202 A265203 * A265205 A265206 A265207

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Dec 04 2015

STATUS

approved

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Last modified October 27 09:08 EDT 2020. Contains 338035 sequences. (Running on oeis4.)