OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
Mikhail R. Gabdullin and Vitalii V. Iudelevich, Numbers of the form kf(k), arXiv:2201.09287 [math.NT] (2022).
Eric Weisstein's World of Mathematics, Distinct Prime Factors
FORMULA
G.f.: Sum_{k>=1} prime(k) * x^prime(k) / (1 - x^prime(k))^2.
a(n) = bigomega(rad(n)^n).
a(n) = Sum_{d|n} A061397(n/d) * d.
Define f(x) = #{n <= x: a(n) <= x}. Gabdullin & Iudelevich show that f(x) ~ x/log log x. - Charles R Greathouse IV, Mar 16 2022
MATHEMATICA
Table[n PrimeNu[n], {n, 1, 70}]
nmax = 70; CoefficientList[Series[Sum[Prime[k] x^Prime[k]/(1 - x^Prime[k])^2, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(Magma) [0] cat [n*(#PrimeDivisors(n)):n in [2..70]]; // Marius A. Burtea, Oct 10 2019
(PARI) a(n)=n*omega(n) \\ Charles R Greathouse IV, Mar 16 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 09 2019
STATUS
approved