



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
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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(n1) implies n is either a prime or the power of a prime.


LINKS



FORMULA

a(n) = a(n1)*(1+n*(P1)/(n1)) if n is the power of any prime (P); a(n) = a(n1) 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



KEYWORD

nonn


AUTHOR

Timothy Frison (frison(AT)gmail.com), Nov 03 2006


EXTENSIONS



STATUS

approved



