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A279911
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a(n) = Sum_{i=1..n} denominator(n^i/i).
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2
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MAPLE
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PROG
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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
(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
(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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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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