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
Links
- Daniel Suteu, Table of n, a(n) for n = 0..10000
Crossrefs
Cf. A279912.
Programs
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Magma
[0] cat [&+[Denominator(n^i/i):i in [1..n]]:n in [1..60]]; // Marius A. Burtea, Jul 29 2019
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Maple
A279911:=n->add(denom(n^i/i), i=1..n): seq(A279911(n), n=0..100);
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PARI
a(n) = sum(k=1, n, if(gcd(n,k) == 1, k, denominator(n^k/k))); \\ Daniel Suteu, Jul 28 2019
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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
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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