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 A124052 a(n) = sigma(lcm(1,2,...,n)) = A000203(A003418(n)). 1
 1, 3, 12, 28, 168, 168, 1344, 2880, 9360, 9360, 112320, 112320, 1572480, 1572480, 1572480, 3249792, 58496256, 58496256, 1169925120, 1169925120, 1169925120, 1169925120, 28078202880, 28078202880, 145070714880, 145070714880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Old definition was: "Sum from 1 to n of all factors of primes less than n such that the power of any factor (p) never exceeds log(n) base p." a(n) > a(n-1) implies n is either a prime or the power of a prime. LINKS Seiichi Manyama, Table of n, a(n) for n = 1..2000 FORMULA a(n) = a(n-1)*(1+n*(P-1)/(n-1)) if n is the power of any prime (P); a(n) = a(n-1) if n is not the power of any prime. - Ridouane Oudra, Aug 28 2019 EXAMPLE a(5) = (1+2+4)*(1+3)*(1+5). a(6) = a(5), since 6 is not a primepower. a(7) = (1+2+4)*(1+3)*(1+5)*(1+7). a(8) = (1+2+4+8)*(1+3)*(1+5)*(1+7). a(9) = (1+2+4+8)*(1+3+9)*(1+5)*(1+7). a(10) = a(9) since 10 is not a primepower. MAPLE with(numtheory): seq(sigma(lcm(`\$`(1 .. n))), n = 1 .. 60); # Ridouane Oudra, Aug 28 2019 PROG (Magma) [DivisorSigma(1, Lcm([1..n])):n in [1..26]]; // Marius A. Burtea, Aug 29 2019 CROSSREFS Cf. A000203, A034699, A003418. Sequence in context: A351643 A034503 A026557 * A215640 A104353 A001860 Adjacent sequences: A124049 A124050 A124051 * A124053 A124054 A124055 KEYWORD nonn AUTHOR Timothy Frison (frison(AT)gmail.com), Nov 03 2006 EXTENSIONS Replaced definition with a simpler one from Ridouane Oudra, Aug 28 2019. - N. J. A. Sloane, Aug 30 2019 STATUS approved

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Last modified December 2 20:20 EST 2023. Contains 367526 sequences. (Running on oeis4.)