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%I #16 May 20 2024 02:30:00
%S 1,22,183,704,2605,4026,14707,22548,44469,57310,147631,128832,344773,
%T 323554,476715,721596,1340977,978318,2352295,1833920,2691381,3247882,
%U 6168163,4126284,8140625,7585006,10806147,10353728,19827445,10487730,27734491,23091212,27016473
%N a(n) = Sum_{k=1..n} sigma_2( (n/gcd(k,n))^2 ).
%H Seiichi Manyama, <a href="/A372996/b372996.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{d|n} phi(d) * sigma_2(d^2).
%F From _Amiram Eldar_, May 20 2024: (Start)
%F Multiplicative with a(p^e) = (p^(5*e+7) - p^(5*e+6) - p^(e+5) + p^e + p^6 - p^2) / ((p^2 - 1) * (p^5 - 1)).
%F Sum_{k=1..n} a(k) ~ c * n^6 / 6, where c = zeta(5) * zeta(6) * Product_{p prime} (1 - 1/p^2 + 1/p^3 - 1/p^4 - 1/p^6 + 1/p^7) = 0.71416166953252012639... . (End)
%t a[n_] := DivisorSum[n, EulerPhi[#] * DivisorSigma[2, #^2] &]; Array[a, 100] (* _Amiram Eldar_, May 20 2024 *)
%o (PARI) a(n) = sumdiv(n, d, eulerphi(d)*sigma(d^2, 2));
%Y Cf. A062380, A372227.
%Y Cf. A013663, A013664.
%K nonn,mult
%O 1,2
%A _Seiichi Manyama_, May 19 2024
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