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Search: id:A000026
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| A000026 |
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Mosaic numbers or multiplicative projection of n.
(Formerly M0467 N0171)
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+0
5
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| 1, 2, 3, 4, 5, 6, 7, 6, 6, 10, 11, 12, 13, 14, 15, 8, 17, 12, 19, 20, 21, 22, 23, 18, 10, 26, 9, 28, 29, 30, 31, 10, 33, 34, 35, 24, 37, 38, 39, 30, 41, 42, 43, 44, 30, 46, 47, 24, 14, 20, 51, 52, 53, 18, 55, 42, 57, 58, 59, 60, 61, 62, 42, 12, 65, 66, 67, 68, 69, 70, 71, 36
(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)=n if n is square-free.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
R. A. Gillman, The Average Size of a Certain Arithmetic Function, A6660 solution, Amer. Math. Monthly 100 (1993) 296-298.
B. Gordon and M. M. Robertson, A theorem on mosaics, Canad. J. Math., 17 (1965), 1010-1014.
A. A. Mullin, Some related number-theoretic functions, Research Problem 4, Bull. Amer. Math. Soc., 69 (1963), 446-447.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
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n = Product (p_j^k_j) -> a(n) = Product (p_j * k_j).
Multiplicative with a(p^e) = p*e. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
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EXAMPLE
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24 = 2^3*3^1, a(24)=2*3*3*1=18.
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MATHEMATICA
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Array[ Times@@Flatten[ FactorInteger[ # ] ]&, 100 ]
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PROGRAM
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(PARI) a(n)=local(f); if(n<1, 0, f=factor(n); prod(k=1, matsize(f)[1], f[k, 1]*f[k, 2]))
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CROSSREFS
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Adjacent sequences: A000023 A000024 A000025 this_sequence A000027 A000028 A000029
Sequence in context: A112264 A017872 A161209 this_sequence A005599 A071934 A161658
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KEYWORD
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nonn,easy,nice,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Example, program, definition, comments and more terms added by Olivier Gerard (02/99).
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