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%I #19 Sep 08 2022 08:46:14
%S 1,3,3,11,3,9,3,25,11,9,3,33,3,9,9,137,3,33,3,33,9,9,3,75,11,9,25,33,
%T 3,27,3,147,9,9,9,121,3,9,9,75,3,27,3,33,33,9,3,411,11,33,9,33,3,75,9,
%U 75,9,9,3,99,3,9,33,1089,9,27,3,33,9,27,3,275,3,9,33,33,9,27,3,411,137,9,3,99,9,9,9,75,3,99,9,33
%N a(n) = lcm_{d|n} tau(d) * Sum_{d|n} 1/tau(d), where tau(d) represents the number of divisors of d (A000005(d)).
%H Antti Karttunen, <a href="/A265390/b265390.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F a(n) = A253139(n) * Sum_{d|n} 1/A000005(d) = A265391(n) * A253139(n) / A265392(n).
%F Multiplicative with a(p^e) = A025529(e+1) = (1/1 + 1/2 + 1/3 + ... + 1/(e+1)) * lcm{1, 2, 3, ..., e+1}.
%e For n = 6; divisors d of 6: {1, 2, 3, 6}; tau(d): {1, 2, 2, 4}; LCM_{d|6} tau(d) = 4; a(6) = 4/1 + 4/2 + 4/2 + 4/4 = 9.
%t Table[LCM @@ DivisorSigma[0, Divisors@ n] Sum[1/DivisorSigma[0, d], {d, Divisors@ n}], {n, 74}] (* _Michael De Vlieger_, Dec 09 2015 *)
%o (Magma) [&+[LCM([NumberOfDivisors(d): d in Divisors(n)]) / NumberOfDivisors(d): d in Divisors(n) ]: n in [1..100]]
%o (PARI)
%o A253139(n) = my(d = divisors(n)); lcm(vector(#d, k, numdiv(d[k]))); \\ This function from _Michel Marcus_, Jan 23 2015
%o A265390(n) = (A253139(n) * sumdiv(n,d,(1/numdiv(d)))); \\ _Antti Karttunen_, Nov 24 2017
%Y Cf. A000005, A025529, A253139, A265391, A265392, A265393.
%K nonn,mult
%O 1,2
%A _Jaroslav Krizek_, Dec 08 2015
%E More terms from _Antti Karttunen_, Nov 24 2017
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