

A343458


Distinct values of the least common multiple of initial segments of numbers of least prime signature (A025487).


2



1, 2, 4, 12, 24, 48, 240, 480, 1440, 2880, 5760, 40320, 120960, 241920, 483840, 2419200, 4838400, 14515200, 29030400, 319334400, 638668800, 1916006400, 3832012800, 7664025600, 38320128000, 498161664000, 996323328000, 6974263296000, 20922789888000, 41845579776000, 83691159552000
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OFFSET

1,2


COMMENTS

The least common multiple of all numbers of least prime signature (A025487) <= c equals the least common multiple of all primorial powers (A100778) <= c, where c is an arbitrary positive real number.
The terms of this sequence are themselves numbers of least prime signature. Write a(n) in its prime factorization, Product_{i=1..k} A000040(i)^e_i. Then e_i is approximately proportional to 1/log_2(A002110(i)).
More precisely, the least common multiple of all numbers of least prime signature (A025487) <= c has prime factorization Product_{i>=1} A000040(i)^e_i, where e_i = floor(log(c)/log(A002110(i))).


LINKS

David A. Corneth, Table of n, a(n) for n = 1..1317


FORMULA

a(1) = 1, a(n) = lcm(a(n1), A100778(n)) for n >= 2.  David A. Corneth, Apr 18 2021


EXAMPLE

The least common multiple of the numbers of least prime signature up through 36 is equal to the least common multiple of all primorial powers up through 36, including 2^5 = 32, 6^2 = 36, and 30^1 = 30. Thus 2^5 * 3^2 * 5 = 1440 is a term of this sequence.


CROSSREFS

Cf. A025487, A100778.
Sequence in context: A181806 A301416 A340137 * A328521 A133411 A201078
Adjacent sequences: A343455 A343456 A343457 * A343459 A343460 A343461


KEYWORD

nonn


AUTHOR

Hal M. Switkay, Apr 15 2021


EXTENSIONS

More terms from David A. Corneth, Apr 18 2021


STATUS

approved



