Search: id:A070829
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%I A070829
%S A070829 1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,
%T A070829 1,0,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0,
%U A070829 0,0,0,0,0,0,0,1,1,1,0
%N A070829 Array showing which primes divide n>=2.
%C A070829 In the Kac reference this array is called rho_{p}(n) := 1 if p divides 
               n else 0.
%C A070829 The row length sequence is A061395(n),n>=2: [1,2,1,3,2,4,1,2,3,5,2,6,
               4,3,...] (the index of the largest prime dividing n). All row entries 
               beyond these numbers are 0, hence they are not shown. The n=1 row 
               would have 0 for all entries.
%C A070829 The column sequences (without leading zeros) give for m>=1 periodic sequences 
               with the period: 1 followed by p(m)-1 zeros. They start with n=p(m) 
               := A000040(m).
%D A070829 Mark Kac, A Personal History of the Scottish Book, pp. 17-27, in R. D. 
               Mauldin (edt.), The Scottish Book, Birkhaeuser, Boston, Basel, 1981.
%H A070829 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/A070829.text">
               First 32 rows</a>.
%F A070829 a(n, m)=1 if p(m), m>=1, divides n>=2, with the prime p(m) := A000040(m), 
               else 0.
%e A070829 {1}, {0, 1}, {1}, {0, 0, 1}, {1, 1}, {0, 0, 0, 1}, {1}, {0, 1}, {1, 0, 
               1}...
%e A070829 Row n=10: {1,0,1} because p(1)=2 and p(3)= 5 divides 10.
%Y A070829 Cf. A067255 (array with multiplicities).
%Y A070829 Sequence in context: A141212 A137893 A108882 this_sequence A118175 A120526 
               A086694
%Y A070829 Adjacent sequences: A070826 A070827 A070828 this_sequence A070830 A070831 
               A070832
%K A070829 nonn,easy,tabf
%O A070829 2,1
%A A070829 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 17, 
               2002

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