A345091 - OEIS

%I #11 Nov 25 2021 12:43:28

%S 1,2,4,6,11,10,22,20,30,26,56,32,79,50,67,72,137,66,172,92,135,122,

%T 254,112,255,170,252,184,407,142,466,272,343,290,431,240,667,362,483,

%U 344,821,282,904,464,561,530,1082,416,1036,530,835,652,1379,522,1115,704,1047,842

%N a(n) = Sum_{k=1..n} k^floor(1/gcd(n,k)).

%H Antti Karttunen, <a href="/A345091/b345091.txt">Table of n, a(n) for n = 1..20000</a>

%F If p is prime, a(p) = Sum_{k=1..p} k^floor(1/gcd(p,k)) = 1^1 + ... + (p-1)^1 + p^0 = p*(p-1)/2 + 1.

%F a(1) = 1, a(n) = n + (n-2)*phi(n)/2 for n >= 2. - _Wesley Ivan Hurt_, Nov 24 2021

%e a(6) = Sum_{k=1..6} k^floor(1/gcd(6,k)) = 1^1 + 2^0 + 3^0 + 4^0 + 5^1 + 6^0 = 1 + 1 + 1 + 1 + 5 + 1 = 10.

%t Table[Sum[k^Floor[1/GCD[n, k]], {k, n}], {n, 80}]

%o (PARI) A345091(n) = if(1==n,n,n + ((n-2)*eulerphi(n)/2)); \\ _Antti Karttunen_, Nov 25 2021

%Y Cf. A000010 (phi), A345090.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 07 2021