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
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Dec 04 2015
STATUS
approved