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Search: id:A113908
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| A113908 |
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Number of prime factors, with multiplicity, of Bell number A000110(n). |
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+0
1
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| 0, 0, 1, 1, 2, 3, 2, 1, 6, 4, 3, 4, 3, 1, 3, 3, 2, 7, 3, 4, 6, 4, 6, 4, 3, 6, 5, 6, 4, 6, 6, 2, 5, 2, 4, 7, 4, 3, 4, 3, 3, 6, 1, 7, 6, 5, 4, 8, 4, 2, 5, 3, 5, 6, 3, 1, 12, 3, 3, 5, 3, 7, 3, 7, 4, 5, 6, 3, 5, 4, 4, 10, 9, 6, 6, 5, 8, 5, 5, 8, 5, 4, 5, 3, 2
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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This is 1 for A051330 (indices of prime Bell numbers) and is 2 for A113883 (indices of semiprime Bell numbers). The records begin a(0) = 0, a(2) = 1, a(4) = 2, a(5) = 3, a(8) = 6, a(17) = 7, a(56) = 12.
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LINKS
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John Sokol, The First 1000 Bell Numbers.
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FORMULA
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a(n) = BigOmega(A000110(n)). a(n) = A001222(A000110(n)).
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EXAMPLE
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a(5) = BigOmega(Bell(5)) = number of prime factors, with multiplicity, of 52 = A001222(52) = A001222(2^2 * 13) = 3.
a(82) = 5 because Bell(82) =
624387 454429 479848 302014 120414 448006 907125 370284 776661 891529 899343 806658 375826 740689 137423 = 3 * 23 * 809 061719 * 2163 974554 206277
733396 620954 093256 346607 * 5168 580384 938902 936990 283741 676942 903899
which, with two prime factors each 40 digits in length, takes the longest to factor of any value less than Bell(85). The second-hardest to this is Bell(75).
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MAPLE
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with(numtheory):with(combinat):a:=proc(n) if n=0 then 0 else bigomega(bell(n)) fi end: seq(a(n), n=0..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 11 2008
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CROSSREFS
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Cf. A000110, A001222, A113015, A113883.
Sequence in context: A055101 A081316 A079893 this_sequence A065369 A167772 A077870
Adjacent sequences: A113905 A113906 A113907 this_sequence A113909 A113910 A113911
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 29 2006
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