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%I #2 Mar 30 2012 17:25:32
%S 2,3,3,4,4,5,5,5,6,6,7,7,7,7,8,8,9,9,9,9,10,10,10,11,11,11,11,12,12,
%T 13,13,13,13,13,13,14,14,15,15,15,15,16,16,16,16,17,17,17,17,17
%N n occurs d(n-1) times.
%F A composite of infinite arithmetic sequences (1 mod k, k>1): (1, 2, 3,...), (1, 3, 5,...), (1, 4, 7,...)...; arranged in order of magnitude; and deleting the initial ones.
%e Given an array of arithmetic sequences: k, (1 mod 2), ( 1 mod 3)...:
%e 1,...2,...3,...4,...
%e 1,...3,...5,...7,...
%e 1,...4,...7,..10,...
%e 1,...5,...9,..13,...
%e ...
%e We extract all terms in the array (>1) and arrange in order of magnitude.
%e n occurs d(n-1) times where d(n) = A000005: (1, 2, 2, 3, 2, 4, 2, 4, 3, 4,...).
%e 7 occurs 4 times in the following subsets, indicated by the divisors of (n-1): (n), (1 mod 2), (1 mod 3), (1 mod 6) = (1, 2, 3, 4, 5, 6, 7,...), (1, 3, 5, 7,...), (1, 4, 7, 10,...) and (1, 7, 13, 19,...).
%Y Cf. A000005.
%K nonn
%O 1,1
%A _Gary W. Adamson_, Aug 21 2008