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 A265390 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)). 7
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(n) = A253139(n) * Sum_{d|n} 1/A000005(d) = A265391(n) * A253139(n) / A265392(n). Multiplicative with a(p^e) = A025529(e+1) = (1/1 + 1/2 + 1/3 + ... + 1/(e+1)) * lcm{1, 2, 3, ..., e+1}. EXAMPLE 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. MATHEMATICA Table[LCM @@ DivisorSigma[0, Divisors@ n] Sum[1/DivisorSigma[0, d], {d, Divisors@ n}], {n, 74}] (* Michael De Vlieger, Dec 09 2015 *) PROG (MAGMA) [&+[LCM([NumberOfDivisors(d): d in Divisors(n)]) / NumberOfDivisors(d): d in Divisors(n) ]: n in [1..100]] (PARI) A253139(n) = my(d = divisors(n)); lcm(vector(#d, k, numdiv(d[k]))); \\ This function from Michel Marcus, Jan 23 2015 A265390(n) = (A253139(n) * sumdiv(n, d, (1/numdiv(d)))); \\ Antti Karttunen, Nov 24 2017 CROSSREFS Cf. A000005, A025529, A253139, A265391, A265392, A265393. Sequence in context: A283220 A101326 A265391 * A276390 A178707 A036391 Adjacent sequences:  A265387 A265388 A265389 * A265391 A265392 A265393 KEYWORD nonn,mult AUTHOR Jaroslav Krizek, Dec 08 2015 EXTENSIONS More terms from Antti Karttunen, Nov 24 2017 STATUS approved

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Last modified May 20 20:16 EDT 2019. Contains 323426 sequences. (Running on oeis4.)