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 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 (list; graph; refs; listen; history; text; internal format)
 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(n-1), 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

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Last modified September 27 01:12 EDT 2021. Contains 347673 sequences. (Running on oeis4.)