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A000026
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Mosaic numbers or multiplicative projection of n.
(Formerly M0467 N0171)
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10
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=n if n is squarefree.
a(A193551(n)) = n and a(m) != n for m < A193551(n). [Reinhard Zumkeller, Aug 27 2011]
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REFERENCES
| R. A. Gillman, The Average Size of a Certain Arithmetic Function, A6660 solution, Amer. Math. Monthly 100 (1993) 296-298.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
B. Gordon and M. M. Robertson, Two theorems 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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FORMULA
| n = Product (p_j^k_j) -> a(n) = Product (p_j * k_j).
Multiplicative with a(p^e) = p*e. - David W. Wilson, Aug 01, 2001.
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EXAMPLE
| 24 = 2^3*3^1, a(24)=2*3*3*1=18.
a(n)=A005361(n)*A007947(n) [From Enrique Perez Herrero, Jun 24 2010]
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MAPLE
| A000026 := proc(n) local e, j; e := ifactors(n)[2]:
mul (e[j][1]*e[j][2], j=1..nops(e)) end:
seq (A000026(n), n=1..80);
# - Peter Luschny, Jan 17 2011
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MATHEMATICA
| Array[ Times@@Flatten[ FactorInteger[ # ] ]&, 100 ]
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PROG
| (PARI) a(n)=local(f); if(n<1, 0, f=factor(n); prod(k=1, matsize(f)[1], f[k, 1]*f[k, 2]))
(Haskell)
a000026 n = f a000040_list n 1 (0^(n-1)) 1 where
f _ 1 q e y = y * e * q
f ps'@(p:ps) x q e y
| m == 0 = f ps' x' p (e+1) y
| e > 0 = f ps x q 0 (y * e * q)
| x < p * p = f ps' 1 x 1 y
| otherwise = f ps x 1 0 y
where (x', m) = divMod x p
a000026_list = map a000026 [1..]
-- Reinhard Zumkeller, Aug 27 2011
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CROSSREFS
| Cf. A008474.
Sequence in context: A112264 A017872 A161209 * A005599 A071934 A161658
Adjacent sequences: A000023 A000024 A000025 * A000027 A000028 A000029
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KEYWORD
| nonn,easy,nice,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Example, program, definition, comments and more terms added by Olivier Gerard (02/99).
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