A344525 a(n) = Sum_{1 <= x_1, x_2, ..., x_n <= n} gcd(x_1, x_2, ..., x_n).

1, 5, 30, 276, 3165, 47521, 826000, 16843792, 387723045, 10009889889, 285360865350, 8918311872516, 302888304741841, 11112685595264369, 437898699063881208, 18447025862624951488, 827242515246907227633, 39346558373191515582161, 1978421007731307479908450, 104857700007507456784458724

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..386

Formula

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

a(n) ~ n^n. - Vaclav Kotesovec, May 23 2021

Mathematica

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

Prog

(PARI) a(n) = sum(k=1, n, eulerphi(k)*(n\k)^n);
(Python)
from sympy import totient
def A344525(n): return sum(totient(k)*(n//k)**n for k in range(1, n+1)) # Chai Wah Wu, Aug 05 2024
(Python)
# uses Python function from A002088
def A344525(n):
    c, j, v = 0, 1, 0
    while j <= n:
        k = n//j
        m = n//k
        c += k**n*(-v+(v:=A002088(m)))
        j = m+1
    return c # Chai Wah Wu, May 15 2026

Crossrefs

Main diagonal of A344479.

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

Sequence in context: A353547 A199131 A342389 * A277464 A258300 A276752

Adjacent sequences: A344522 A344523 A344524 * A344526 A344527 A344528

Keyword

nonn,easy

Author

Seiichi Manyama, May 22 2021

Status

approved