A344525 - OEIS

%I #21 Aug 05 2024 09:39:25

%S 1,5,30,276,3165,47521,826000,16843792,387723045,10009889889,

%T 285360865350,8918311872516,302888304741841,11112685595264369,

%U 437898699063881208,18447025862624951488,827242515246907227633,39346558373191515582161

%N a(n) = Sum_{1 <= x_1, x_2, ... , x_n <= n} gcd(x_1,x_2, ... ,x_n).

%H Seiichi Manyama, <a href="/A344525/b344525.txt">Table of n, a(n) for n = 1..386</a>

%F a(n) = Sum_{k=1..n} phi(k) * floor(n/k)^n.

%F a(n) ~ n^n. - _Vaclav Kotesovec_, May 23 2021

%t a[n_] := Sum[EulerPhi[k] * Quotient[n, k]^n, {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, May 22 2021 *)

%o (PARI) a(n) = sum(k=1, n, eulerphi(k)*(n\k)^n);

%o (Python)

%o from sympy import totient

%o def A344525(n): return sum(totient(k)*(n//k)**n for k in range(1,n+1)) # _Chai Wah Wu_, Aug 05 2024

%Y Main diagonal of A344479.

%Y Cf. A018806, A344140, A344522, A344523, A344524.

%K nonn

%O 1,2

%A _Seiichi Manyama_, May 22 2021