A124052 a(n) = sigma(lcm(1,2,...,n)) = A000203(A003418(n)).

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

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