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%I #13 Mar 13 2021 10:05:04
%S 1,3,7,13,21,39,43,81,109,173,111,475,157,507,1107,1153,273,2997,343,
%T 6133,6685,3479,507,30819,13001,10533,44227,65071,813,234959,931,
%U 215553,368265,136241,414183,1991281,1333,531471,3215947,4883141,1641,12951117,1807,12735043,36892689,8401259
%N a(n) = Sum_{k=1..n} (n/gcd(k,n))^gcd(k,n).
%H Seiichi Manyama, <a href="/A342422/b342422.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = Sum_{d|n} phi(d^(n/d+1)) = Sum_{d|n} phi(d) * d^(n/d).
%t a[n_] := Sum[(n/GCD[k, n])^GCD[k, n], {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, Mar 11 2021 *)
%o (PARI) a(n) = sum(k=1, n, (n/gcd(k, n))^gcd(k, n));
%o (PARI) a(n) = sumdiv(n, d, eulerphi(d^(n/d+1)));
%o (PARI) a(n) = sumdiv(n, d, eulerphi(d)*d^(n/d));
%Y Cf. A000010, A342421.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Mar 11 2021
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