A279911 a(n) = Sum_{k=0..n} k / gcd(n^k, k).

0, 1, 2, 4, 6, 11, 10, 22, 22, 31, 28, 56, 36, 79, 58, 72, 86, 137, 80, 172, 112, 145, 148, 254, 146, 261, 208, 274, 230, 407, 182, 466, 342, 375, 360, 448, 322, 667, 456, 528, 444, 821, 384, 904, 592, 635, 676, 1082, 574, 1051, 692, 924, 836, 1379, 732, 1154, 912, 1153

Offset

0,3

Links

Daniel Suteu, Table of n, a(n) for n = 0..10000

Formula

a(n) = Sum_{i=1..n} denominator(n^i/i). [Original name.]

From Daniel Suteu, Jul 28 2019: (Start)

a(prime(n)) = A072205(n).

a(p^k) = (p^(2*k+1) + p + 2) / (2*(p+1)), for prime powers p^k.

a(n) = Sum_{k=1..n} gcd(m, k), where m = A095996(n).

a(n) = Sum_{k=1..n} f(n,k), where f(n,k) is the largest divisor d of k for which gcd(d, n) = 1. (End)

a(n) = Sum_{1<=k<=n, gcd(n,k)=1} phi(k)*floor(n/k). - Ridouane Oudra, May 24 2023

a(n) = (1/2) * Sum_{m=1..n, rad(m)|rad(n)} A023900(m) * floor(n/m) * (1+floor(n/m)). - Daniel Suteu, May 11 2026

Maple

A279911:=n->add(denom(n^i/i), i=1..n): seq(A279911(n), n=0..100);
seq(add(k/igcd(n^k, k), k=0..n), n=0..57); # Peter Luschny, Sep 29 2025

Prog

(PARI) a(n) = my(f = factor(n), ps = f[, 1]~, r = #ps, res=0); forvec(e = vector(r, i, [0, logint(n, ps[i])]), my(m = prod(i=1, r, ps[i]^e[i])); my(q = n\m, lam = prod(i=1, r, if(e[i]>0, 1-ps[i], 1))); res += lam * q*(q+1)/2); res; \\ Daniel Suteu, May 11 2026
(Magma) [0] cat [&+[Denominator(n^i/i):i in [1..n]]:n in [1..60]]; // Marius A. Burtea, Jul 29 2019

Crossrefs

Cf. A279912.

Sequence in context: A303752 A304532 A345091 * A063183 A057661 A237277

Adjacent sequences: A279908 A279909 A279910 * A279912 A279913 A279914

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 22 2016

Extensions

New name by Peter Luschny, Sep 29 2025

Status

approved