%I #10 May 31 2013 07:51:49

%S 1,1,2,3,3,4,4,4,4,5,5,6,6,7,6,6,6,7,7,8,7,7,7,8,8,8,8,9,9,9,9,10,10,

%T 10,10,10,9,10,11,11,10,11,10,12,12,12,12,13,12,13,13,13,12,13,13,13,

%U 12,12,12,13,13,14,13,13,14,14,13,14,13,13,13,14,14

%N a(n) = Number of distinct values in column n of A225630.

%C Also, for n>=1, a(n) = the length of n-th row of A225632.

%C For the positions of records, and other remarks, see comments at A225633.

%F a(n) = A225638(n)+A226056(n).

%F a(n) = A225633(n) + 1.

%o (Scheme):

%o (define (A225634 n) (count_number_of_distinct_lcms_of_partitions_until_fixed_point_met n 1))

%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. A225635 (partial sums).

%Y Cf. A225644, A225653, A225654.

%K nonn

%O 0,3

%A _Antti Karttunen_, May 13 2013