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%I #13 Jun 05 2013 21:22:30
%S 1,1,1,2,2,3,3,3,3,4,4,5,5,6,5,5,5,6,5,7,6,7,6,7,7,7,7,8,8,8,9,9,9,10,
%T 9,10,9,9,10,10,10,10,10,11,12,11,11,12,12,11,11,13,12,12,12,12,12,12,
%U 12,12,13,13,13,13,12,14,13,13,13,13,13,13,14,14,15
%N a(n) = number of distinct values in column n of A225640.
%C For the positions of records, and other remarks, see comments at A225643.
%F a(n) = A225643(n) + 1.
%F a(n) = A225639(n) + A226056(n).
%o (Scheme):
%o (define (A225644 n) (count_number_of_distinct_lcms_of_partitions_until_fixed_point_met n n))
%o (define (count_number_of_distinct_lcms_of_partitions_until_fixed_point_met n initial_value) (let loop ((lcms (list initial_value initial_value))) (fold_over_partitions_of n 1 lcm (lambda (p) (set-car! lcms (max (car lcms) (lcm (second lcms) p))))) (if (= (car lcms) (second lcms)) (length (cdr lcms)) (loop (cons (car lcms) lcms)))))
%o (define (fold_over_partitions_of m initval addpartfun colfun) (let recurse ((m m) (b m) (n 0) (partition initval)) (cond ((zero? m) (colfun partition)) (else (let loop ((i 1)) (recurse (- m i) i (+ 1 n) (addpartfun i partition)) (if (< i (min b m)) (loop (+ 1 i))))))))
%Y Cf. A225645 (partial sums).
%Y Cf. A225634, A225653, A225654, A225639, A226056.
%K nonn
%O 0,4
%A _Antti Karttunen_, May 15 2013
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