OFFSET
1,2
FORMULA
a(n) = numerator of Sum_{d|n} phi(n/d) / d.
a(n) = numerator of Sum_{k=1..n} 1 / gcd(n,k).
a(n) = numerator of sigma_2(n^2) / (n * sigma_1(n^2)).
a(p) = p^2 - p + 1 where p is prime.
From Amiram Eldar, Nov 21 2022: (Start)
a(n) = numerator(A057660(n)/n).
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 = 55; CoefficientList[Series[Sum[EulerPhi[k] Log[1/(1 - x^k)], {k, 1, nmax}], {x, 0, nmax}], x] // Numerator // Rest
Table[Sum[EulerPhi[n/d]/d, {d, Divisors[n]}], {n, 55}] // Numerator
Table[Sum[1/GCD[n, k], {k, n}], {n, 55}] // Numerator
Table[DivisorSigma[2, n^2]/(n DivisorSigma[1, n^2]), {n, 55}] // Numerator
PROG
(PARI) a(n) = numerator(sumdiv(n, d, eulerphi(n/d) / d)); \\ Michel Marcus, Apr 03 2020
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ilya Gutkovskiy, Apr 02 2020
STATUS
approved