This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A069201 #38 Sep 08 2022 08:45:05
%S A069201 1,3,5,5,7,11,13,13,13,17,19,19,21,25,29,29,31,31,33,33,37,41,43,43,
%T A069201 43,47,47,47,49,57,59,59,63,67,71,71,73,77,81,81,83,91,93,93,93,97,99,
%U A069201 99,99,99,103,103,105,105,109,109,113,117,119,119,121,125,125,125,129,137
%N A069201 a(n) = Sum_{k=1..n} mu(k)^2 * 2^omega(k) where omega(k) is the number of distinct primes in the factorization of k.
%D A069201 G. Tenenbaum and Jie Wu, Cours Spécialisés No. 2: "Théorie analytique et probabiliste des nombres", Collection SMF, Ordres moyens, p. 20.
%H A069201 Antti Karttunen, <a href="/A069201/b069201.txt">Table of n, a(n) for n = 1..10000</a>
%H A069201 Vaclav Kotesovec, <a href="/A069201/a069201.jpg">Graph - the asymptotic ratio (1000000 terms)</a>
%F A069201 Asymptotic formula: a(n) = C*n*log(n) + O(n) with C = Product_{p prime} (1 - 1/p)^2*(1 + 2/p).
%F A069201 The constant C is A065473. - _Amiram Eldar_, May 24 2020
%F A069201 a(n) = Sum_{k=1..n} mu(k)^2*d(k), where d is the number of divisors function (A000005). - _Ridouane Oudra_, Jul 25 2019
%F A069201 More precise asymptotics: Let f(s) = Product_{primes p} (1 - 3/p^(2*s) + 2/p^(3*s)), then a(n) ~ n*(f(1)*(log(n) + 2*gamma - 1) + f'(1)), where f(1) = A065473, f'(1) = f(1) * Sum_{primes p} 6*log(p)/(p^2 + p - 2) = 0.802323384763097462846799913287578352653695442033314074501634920897596526... and gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Aug 20 2021
%p A069201 with(numtheory): seq(add(tau(k)*mobius(k)^2, k=1..n), n=1..90); # _Ridouane Oudra_, Jul 25 2019
%t A069201 Accumulate @ Table[MoebiusMu[n]^2 * 2^PrimeNu[n], {n, 1, 66}] (* _Amiram Eldar_, May 24 2020 *)
%o A069201 (Scheme) (define (A069201 n) (if (= 1 n) n (+ (A074823 n) (A069201 (- n 1))))) ;; _Antti Karttunen_, Jul 23 2017
%o A069201 (PARI) a(n) = sum(k=1, n, moebius(k)^2*2^omega(k)); \\ _Michel Marcus_, Jul 23 2017
%o A069201 (Magma) [&+[MoebiusMu(k)^2*#Divisors(k):k in [1..n]]: n in [1..66]]; // _Marius A. Burtea_, Jul 27 2019
%Y A069201 Partial sums of A074823.
%Y A069201 Cf. A008966, A034444, A065473, A347149.
%K A069201 easy,nonn
%O A069201 1,2
%A A069201 _Benoit Cloitre_, Apr 14 2002