A225644 a(n) = number of distinct values in column n of A225640.

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, 9, 10, 9, 9, 10, 10, 10, 10, 10, 11, 12, 11, 11, 12, 12, 11, 11, 13, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 12, 14, 13, 13, 13, 13, 13, 13, 14, 14, 15

Offset

0,4

Comments

For the positions of records, and other remarks, see comments at A225643.

Links

Table of n, a(n) for n=0..74.

Formula

a(n) = A225643(n) + 1.

a(n) = A225639(n) + A226056(n).

Prog

(Scheme):
(define (A225644 n) (count_number_of_distinct_lcms_of_partitions_until_fixed_point_met n n))
(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))))))))

Crossrefs

Cf. A225645 (partial sums).

Cf. A225634, A225653, A225654, A225639, A226056.

Sequence in context: A377899 A285507 A103264 * A225633 A060960 A073642

Adjacent sequences: A225641 A225642 A225643 * A225645 A225646 A225647

Keyword

nonn

Author

Antti Karttunen, May 15 2013

Status

approved