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A333696
Denominators of coefficients in expansion of Sum_{k>=1} phi(k) * log(1/(1 - x^k)).
1
1, 2, 3, 4, 5, 2, 7, 8, 9, 10, 11, 12, 13, 14, 5, 16, 17, 6, 19, 20, 3, 22, 23, 24, 25, 26, 27, 28, 29, 10, 31, 32, 11, 34, 5, 36, 37, 38, 39, 40, 41, 2, 43, 4, 15, 46, 47, 16, 49, 50, 17, 52, 53, 18, 55, 56, 57, 58, 59, 20, 61, 62, 63, 64, 65, 22, 67, 68, 23, 10
OFFSET
1,2
FORMULA
a(n) = denominator of Sum_{d|n} phi(n/d) / d.
a(n) = denominator of Sum_{k=1..n} 1 / gcd(n,k).
a(n) = denominator of sigma_2(n^2) / (n * sigma_1(n^2)).
EXAMPLE
1, 3/2, 7/3, 11/4, 21/5, 7/2, 43/7, 43/8, 61/9, 63/10, 111/11, 77/12, 157/13, 129/14, 49/5, ...
MATHEMATICA
nmax = 70; CoefficientList[Series[Sum[EulerPhi[k] Log[1/(1 - x^k)], {k, 1, nmax}], {x, 0, nmax}], x] // Denominator // Rest
Table[Sum[EulerPhi[n/d]/d, {d, Divisors[n]}], {n, 70}] // Denominator
Table[Sum[1/GCD[n, k], {k, n}], {n, 70}] // Denominator
Table[DivisorSigma[2, n^2]/(n DivisorSigma[1, n^2]), {n, 70}] // Denominator
PROG
(PARI) a(n) = denominator(sumdiv(n, d, eulerphi(n/d) / d)); \\ Michel Marcus, Apr 03 2020
CROSSREFS
Sequence in context: A053626 A348990 A348968 * A134364 A338579 A308830
KEYWORD
nonn,frac
AUTHOR
Ilya Gutkovskiy, Apr 02 2020
STATUS
approved