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%I #14 Jul 29 2012 21:53:32
%S 0,1,1,1,2,1,2,1,1,2,1,2,1,1,1,2,3,2,1,1,2,1,2,1,3,2,1,1,1,1,1,2,2,1,
%T 2,1,2,1,3,1,1,2,3,1,2,2,1,2,1,3,1,2,1,2,2,3,1,4,1,1,2,1,1,1,1,3,2,1,
%U 2,2,1,3,2,1,3,3,1,1,2,1,3,2,2,4,1,3,2,1,2,1,3,1,2,1,2,1,2,2,1,2
%N Irregular triangle read by rows n lists the values k of all decompositions of 2n into unordered sums of two k-almost primes.
%C Row n has 1+A214154(n) entries, if n <> 1, where the '1' means the splitting 2*n=n+n into non-distinct k-almost primes is also registered here, but not in A214154. Therefore the last entry in row n is A001222(n) for n > 3.
%C Row sums are 0, 1, 1, 3, 4, 3, 4, 7, 6, 9, 3, 10, 8, 9, 12, 13, 6, 16, 10, 19, 12, 11, 9, 25, 16, 16, 15, 19, 14, 31, 14, 30, 14, 15, 24,..
%e If written as a triangle:
%e 0,
%e 1,
%e 1,
%e 1, 2,
%e 1, 2, 1,
%e 1, 2,
%e 1, 2, 1,
%e 1, 1, 2, 3,
%e 2, 1, 1, 2,
%e 1, 2, 1, 3, 2,
%e 1, 1, 1,
%e 1, 1, 2, 2, 1, 3,
%e 1, 2, 1, 3, 1,
%e 1, 2, 3, 1, 2,
%e 2, 1, 2, 1, 3, 1, 2,
%e 1, 2, 2, 3, 1, 4,
%e 1, 1, 2, 1, 1,
%e 1, 1, 3, 2, 1, 2, 2, 1, 3.
%Y Cf. A078840. - _N. J. A. Sloane_, Jul 29 2012
%K nonn,tabf,less
%O 1,5
%A _Juri-Stepan Gerasimov_, Jul 23 2012
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