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A265204
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Sum of phi(i) over squarefree numbers i <= n.
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1
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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)
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OFFSET
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1,2
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COMMENTS
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Partial sums of absolute values of A097945. - Robert Israel, Dec 10 2015
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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MAPLE
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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
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MATHEMATICA
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Table[Sum[EulerPhi@ i, {i, Select[Range@ n, SquareFreeQ]}], {n, 70}] (* Michael De Vlieger, Dec 10 2015 *)
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PROG
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(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
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CROSSREFS
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Cf. A000010, A097945.
Sequence in context: A039879 A125204 A241386 * A073420 A034408 A227333
Adjacent sequences: A265201 A265202 A265203 * A265205 A265206 A265207
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KEYWORD
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nonn
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AUTHOR
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Jeffrey Shallit, Dec 04 2015
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STATUS
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approved
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