A225634 a(n) = Number of distinct values in column n of A225630.

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, 10, 10, 10, 9, 10, 11, 11, 10, 11, 10, 12, 12, 12, 12, 13, 12, 13, 13, 13, 12, 13, 13, 13, 12, 12, 12, 13, 13, 14, 13, 13, 14, 14, 13, 14, 13, 13, 13, 14, 14

Offset: 0

Author

Antti Karttunen, May 13 2013

Keywords

• nonn

Comments

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

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

Crossrefs

Cf. A225635 (partial sums).

Cf. A225644, A225653, A225654.

Programs

Scheme

(define (A225634 n) (count_number_of_distinct_lcms_of_partitions_until_fixed_point_met n 1))
(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)))))
(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))))))))

Formula

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

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