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%I #20 Oct 28 2022 07:15:03
%S 1,3,7,13,21,21,43,53,64,63,111,91,157,129,147,213,273,192,343,273,
%T 301,333,507,371,526,471,577,559,813,441,931,853,777,819,903,832,1333,
%U 1029,1099,1113,1641,903,1807,1443,1344,1521,2163,1491,2108,1578,1911,2041
%N a(n) = Sum_{d|n} (n/d)*phi(n)/phi(d).
%H Amiram Eldar, <a href="/A069194/b069194.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = p^e*(p^e - p^(e-1)) + (p^(2*e) - 1)/(p^2 - 1). - _Amiram Eldar_, Sep 15 2019
%F Sum_{k=1..n} a(k) ~ c * n^3, where c = (zeta(3)/3) * Product_{p prime} (1 - 1/p^2 + 1/p^5) = 0.2550149528... . - _Amiram Eldar_, Oct 28 2022
%p for i from 1 to 100 do d := divisors(i): a[i] := i*phi(i)*sum(1/d[j]/phi(d[j]),j=1..nops(d)) od:seq(a[j],j=1..100);
%t f[p_, e_] := p^e*(p^e - p^(e-1)) + (p^(2*e) - 1)/(p^2 - 1) ; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Sep 15 2019 *)
%o (Magma) [&+[(n div d)*EulerPhi(n) div EulerPhi(d):d in Divisors(n)]:n in [1..52]]; // _Marius A. Burtea_, Sep 15 2019
%o (PARI) a(n) = sumdiv(n, d, n/d*eulerphi(n)/eulerphi(d)); \\ _Michel Marcus_, Sep 15 2019
%Y Cf. A000010, A002117.
%K mult,easy,nonn
%O 1,2
%A _Vladeta Jovovic_, Apr 10 2002
%E More terms from _Sascha Kurz_, Jan 03 2003
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