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%I #22 Oct 30 2022 03:49:38
%S 1,4,9,18,25,36,49,78,87,100,121,162,169,196,225,326,289,348,361,450,
%T 441,484,529,702,645,676,807,882,841,900,961,1334,1089,1156,1225,1566,
%U 1369,1444,1521,1950,1681,1764,1849,2178,2175,2116,2209,2934,2443,2580
%N Multiplicative with a(p^e) = (p^(2*e+2)-p^(e+1)-p^e+p)/(p^2-1).
%C If k is squarefree (cf. A005117) then A062952(k) = k^2. - _Benoit Cloitre_, Apr 16 2002
%H Amiram Eldar, <a href="/A062952/b062952.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{d|n} phi(d)*sigma(d).
%F a(n) = Sum_{k=1..n} sigma(n/gcd(n, k)).
%F Sum_{k=1..n} a(k) ~ c * n^3, where c = (zeta(2)*zeta(3)/3) * Product_{p prime} (1 - 1/p^2 - 1/p^3 + 1/p^4) = A183699 * A330523 / 3. - _Amiram Eldar_, Oct 30 2022
%t f[p_, e_] := (p^(2*e+2)-p^(e+1)-p^e+p)/(p^2-1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 50] (* _Amiram Eldar_, Jul 31 2019 *)
%o (PARI) a(n) = sumdiv(n, d, eulerphi(d)*sigma(d)) \\ _Michel Marcus_, Jun 17 2013
%Y Cf. A005117, A029939, A057660, A062952.
%Y Cf. A002117, A013661, A183699, A330523.
%K nonn,mult
%O 1,2
%A _Vladeta Jovovic_, Jul 21 2001
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