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Search: id:A069626
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| A069626 |
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Number of distinct sets of numbers whose least common multiple is n. |
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+0
1
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| 1, 1, 1, 2, 1, 5, 1, 4, 2, 5, 1, 22, 1, 5, 5, 8, 1, 22, 1, 22, 5, 5, 1, 92, 2, 5, 4, 22, 1, 109, 1, 16, 5, 5, 5, 200, 1, 5, 5, 92, 1, 109, 1, 22, 22, 5, 1, 376, 2, 22, 5, 22, 1, 92, 5, 92, 5, 5, 1, 1874, 1, 5, 22, 32, 5, 109, 1, 22, 5, 109, 1, 1696, 1, 5, 22, 22, 5, 109, 1, 376, 8, 5, 1, 1874, 5, 5, 5, 92, 1, 1874, 5, 22
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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(1,n) counts as one such set and 1 may not occur in any other set.
a(p) = 1, a(p*q) = 5, a(p^2*q) = 13, a(p^3) =4, a(p^4)= 8 etc. where p and q are primes. It can be shown that a(p^k) = 2^(k-1). Problem: find an expression for a(N) when N = p^a*q^b*r^c..., p,q,r are primes.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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a(n) = sum_{ d divides n } mu(n/d)*2^(tau(d)-1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 07 2003
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EXAMPLE
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a(6) = 5 as the five distinct sets are (1, 6), (2, 6), (3, 6), (2, 3) and (2, 3, 6).
a(12) = 22 from (1,12), (4,3), (2,4,3), (4,6), (2,4,6), (4,3,6), (2,4,3,6), (2,12), (4,12), (2,4,12), (3,12), (2,3,12), (4,3,12), (2,4,3,12), (6,12), (2,6,12), (4,6,12), (2,4,6,12), (3,6,12), (2,3,6,12), (4,3,6,12), (2,4,3,6,12).
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CROSSREFS
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Sequence in context: A055972 A079168 A055205 this_sequence A069359 A014652 A060448
Adjacent sequences: A069623 A069624 A069625 this_sequence A069627 A069628 A069629
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 27 2002
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EXTENSIONS
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Corrected and extended by Naohiro Nomoto (n_nomoto(AT)yabumi.com), Apr 25 2002
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