A343458 Distinct values of the least common multiple of initial segments of numbers of least prime signature (A025487).

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

Offset: 1

Author

Hal M. Switkay, Apr 15 2021

Keywords

• nonn

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))).

Examples

			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.
		

Links

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

Crossrefs

Cf. A025487, A100778.

Formula

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

Extensions

More terms from David A. Corneth, Apr 18 2021