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%I #17 Jul 14 2023 08:52:56
%S 0,2,3,4,5,12,7,8,9,20,11,24,13,28,30,16,17,36,19,40,42,44,23,48,25,
%T 52,27,56,29,90,31,32,66,68,70,72,37,76,78,80,41,126,43,88,90,92,47,
%U 96,49,100,102,104,53,108,110,112,114,116,59,180,61,124,126,64,130,198,67,136,138,210
%N a(n) = n * omega(n).
%H Seiichi Manyama, <a href="/A328260/b328260.txt">Table of n, a(n) for n = 1..10000</a>
%H Mikhail R. Gabdullin and Vitalii V. Iudelevich, <a href="https://arxiv.org/abs/2201.09287">Numbers of the form kf(k)</a>, arXiv:2201.09287 [math.NT] (2022).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%F G.f.: Sum_{k>=1} prime(k) * x^prime(k) / (1 - x^prime(k))^2.
%F a(n) = bigomega(rad(n)^n).
%F a(n) = Sum_{d|n} A061397(n/d) * d.
%F 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
%t Table[n PrimeNu[n], {n, 1, 70}]
%t nmax = 70; CoefficientList[Series[Sum[Prime[k] x^Prime[k]/(1 - x^Prime[k])^2, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o (Magma) [0] cat [n*(#PrimeDivisors(n)):n in [2..70]]; // _Marius A. Burtea_, Oct 10 2019
%o (PARI) a(n)=n*omega(n) \\ _Charles R Greathouse IV_, Mar 16 2022
%Y Cf. A001221, A001222, A007947, A038040, A061397, A066959, A069359, A246655 (fixed points), A293548, A298473.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Oct 09 2019
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