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%I #25 Sep 08 2022 08:45:28
%S 1,3,12,28,168,168,1344,2880,9360,9360,112320,112320,1572480,1572480,
%T 1572480,3249792,58496256,58496256,1169925120,1169925120,1169925120,
%U 1169925120,28078202880,28078202880,145070714880,145070714880
%N a(n) = sigma(lcm(1,2,...,n)) = A000203(A003418(n)).
%C 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."
%C a(n) > a(n-1) implies n is either a prime or the power of a prime.
%H Seiichi Manyama, <a href="/A124052/b124052.txt">Table of n, a(n) for n = 1..2000</a>
%F 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
%e a(5) = (1+2+4)*(1+3)*(1+5).
%e a(6) = a(5), since 6 is not a primepower.
%e a(7) = (1+2+4)*(1+3)*(1+5)*(1+7).
%e a(8) = (1+2+4+8)*(1+3)*(1+5)*(1+7).
%e a(9) = (1+2+4+8)*(1+3+9)*(1+5)*(1+7).
%e a(10) = a(9) since 10 is not a primepower.
%p with(numtheory): seq(sigma(lcm(`$`(1 .. n))), n = 1 .. 60); # _Ridouane Oudra_, Aug 28 2019
%o (Magma) [DivisorSigma(1,Lcm([1..n])):n in [1..26]]; // _Marius A. Burtea_, Aug 29 2019
%Y Cf. A000203, A034699, A003418.
%K nonn
%O 1,2
%A Timothy Frison (frison(AT)gmail.com), Nov 03 2006
%E Replaced definition with a simpler one from _Ridouane Oudra_, Aug 28 2019. - _N. J. A. Sloane_, Aug 30 2019