Search: id:A000026
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%I A000026 M0467 N0171
%S A000026 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,
%T A000026 28,29,30,31,10,33,34,35,24,37,38,39,30,41,42,43,44,30,46,47,24,14,20,
%U A000026 51,52,53,18,55,42,57,58,59,60,61,62,42,12,65,66,67,68,69,70,71,36
%N A000026 Mosaic numbers or multiplicative projection of n.
%C A000026 a(n)=n if n is square-free.
%D A000026 R. A. Gillman, The Average Size of a Certain Arithmetic Function, A6660 
               solution, Amer. Math. Monthly 100 (1993) 296-298.
%D A000026 B. Gordon and M. M. Robertson, A theorem on mosaics, Canad. J. Math., 
               17 (1965), 1010-1014.
%D A000026 A. A. Mullin, Some related number-theoretic functions, Research Problem 
               4, Bull. Amer. Math. Soc., 69 (1963), 446-447.
%D A000026 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000026 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000026 T. D. Noe, <a href="b000026.txt">Table of n, a(n) for n = 1..10000</a>
%F A000026 n = Product (p_j^k_j) -> a(n) = Product (p_j * k_j).
%F A000026 Multiplicative with a(p^e) = p*e. - David W. Wilson (davidwwilson(AT)comcast.net), 
               Aug 01, 2001.
%e A000026 24 = 2^3*3^1, a(24)=2*3*3*1=18.
%t A000026 Array[ Times@@Flatten[ FactorInteger[ # ] ]&, 100 ]
%o A000026 (PARI) a(n)=local(f); if(n<1,0,f=factor(n); prod(k=1,matsize(f)[1],f[k,
               1]*f[k,2]))
%Y A000026 Sequence in context: A112264 A017872 A161209 this_sequence A005599 A071934 
               A161658
%Y A000026 Adjacent sequences: A000023 A000024 A000025 this_sequence A000027 A000028 
               A000029
%K A000026 nonn,easy,nice,mult
%O A000026 1,2
%A A000026 N. J. A. Sloane (njas(AT)research.att.com).
%E A000026 Example, program, definition, comments and more terms added by Olivier 
               Gerard (02/99).

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