A279911 a(n) = Sum_{i=1..n} denominator(n^i/i).

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

Author

Wesley Ivan Hurt, Dec 22 2016

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A279912.

Programs

Magma

[0] cat [&+[Denominator(n^i/i):i in [1..n]]:n in [1..60]]; // Marius A. Burtea, Jul 29 2019

Maple

A279911:=n->add(denom(n^i/i), i=1..n): seq(A279911(n), n=0..100);

PARI

a(n) = sum(k=1, n, if(gcd(n,k) == 1, k, denominator(n^k/k))); \\ Daniel Suteu, Jul 28 2019

PARI

a(n) = sum(k=1, n, if(gcd(n,k) == 1, k, vecmax(select(d->gcd(d, n) == 1, divisors(k))))); \\ Daniel Suteu, Jul 28 2019

PARI

a(n) = my(f=factor(n)[,1]); sum(k=1, n, if(gcd(n, k) == 1, k, gcd(vector(#f, j, k / f[j]^valuation(k, f[j]))))); \\ Daniel Suteu, Jul 29 2019

Formula

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