A345091 a(n) = Sum_{k=1..n} k^floor(1/gcd(n,k)).

1, 2, 4, 6, 11, 10, 22, 20, 30, 26, 56, 32, 79, 50, 67, 72, 137, 66, 172, 92, 135, 122, 254, 112, 255, 170, 252, 184, 407, 142, 466, 272, 343, 290, 431, 240, 667, 362, 483, 344, 821, 282, 904, 464, 561, 530, 1082, 416, 1036, 530, 835, 652, 1379, 522, 1115, 704, 1047, 842

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

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.

a(1) = 1, a(n) = n + (n-2)*phi(n)/2 for n >= 2. - Wesley Ivan Hurt, Nov 24 2021

Example

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.

Mathematica

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

Prog

(PARI) A345091(n) = if(1==n, n, n + ((n-2)*eulerphi(n)/2)); \\ Antti Karttunen, Nov 25 2021

Crossrefs

Cf. A000010 (phi), A345090.

Sequence in context: A088906 A303752 A304532 * A279911 A063183 A057661

Adjacent sequences: A345088 A345089 A345090 * A345092 A345093 A345094

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 07 2021

Status

approved