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Search: id:A055932
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| A055932 |
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Numbers with property that all prime divisors are consecutive primes starting at 2. |
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+0
26
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| 1, 2, 4, 6, 8, 12, 16, 18, 24, 30, 32, 36, 48, 54, 60, 64, 72, 90, 96, 108, 120, 128, 144, 150, 162, 180, 192, 210, 216, 240, 256, 270, 288, 300, 324, 360, 384, 420, 432, 450, 480, 486, 512, 540, 576, 600, 630, 648, 720, 750, 768, 810, 840, 864, 900, 960, 972
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) is also the sorted version of A057335 which is generated recursively using the formula A057335 = A057334 * A057335(repeated), where A057334 = A000040(A000120). - Alford Arnold (arnold1940(AT)aol.com), Nov 11 2001
Square-free kernels of these numbers are primorial numbers. See A080404. - Labos E. (labos(AT)ana.sote.hu), Mar 19 2003
If u and v are terms then so is u*v. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 24 2004
Except for the initial value a(0) = 1, a(n) gives the canonical primal code of the n-th finite sequence of positive integers, where n = (prime_1)^c_1 * ... * (prime_k)^c_k is the code for the finite sequence c_1, ..., c_k. See examples of primal codes at A106177. - Jon Awbrey (jawbrey(AT)att.net), Jun 22 2005
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LINKS
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Franklin T. Adams-Watters, Table of n, a(n) for n = 1..1001
Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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60 is included because 60 = 2^2 * 3 * 5 and 2, 3 and 5 are consecutive primes beginning at 2.
Sequence A057335 begins
1..2..4..6..8..12..18..30..16..24..36..60..54..90..150..210... which is equal to
1..2..2..3..2...3...3...5...2...3...3...5...3...5....5....7... times
1..1..2..2..4...4...6...6...8...8..12..12..18..18...30...30...
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MATHEMATICA
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Select[Range[1000], #==1||FactorInteger[ # ][[ -1, 1]]==Prime[Length[FactorInteger[ # ]]]&]
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CROSSREFS
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Cf. A057335, A056808, A025487, A007947, A002110, A080404, A106177.
Cf. A124829, A124830, A124831, A124833.
Sequence in context: A140110 A128397 A120383 this_sequence A140067 A067946 A145853
Adjacent sequences: A055929 A055930 A055931 this_sequence A055933 A055934 A055935
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet Jul 17 2000
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