A225633 -id:A225633 - cp's OEIS frontend

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

Antti Karttunen, May 13 2013

nonn

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.

Cf. A225635 (partial sums).

Cf. A225644, A225653, A225654.

(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))))))))

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

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

A225629 a(n) = Last value in column n of A225630 which is not yet the fixed point A003418(n) of that column.

Original entry on oeis.org

1, 1, 1, 3, 4, 30, 30, 84, 120, 1260, 840, 13860, 13860, 180180, 180180, 180180, 240240, 6126120, 6126120, 116396280, 58198140, 116396280, 116396280, 2677114440, 2677114440, 13385572200, 13385572200, 40156716600, 40156716600, 776363187600, 776363187600

Offset: 0

Antti Karttunen, May 13 2013

nonn

a(n) = also the second rightmost terms of row n of irregular table A225632.

a(0)= a(1) = 1 by convention.

Cf. A225630, A225637.

(define (A225629 n) (A225630bi n (max 0 (- (A225633 n) 1))))

a(n) = A225630(n,max(0,A225633(n)-1)).

A225643 Number of steps to reach a fixed point (A003418(n)), when starting from partition {n} of n and continuing with the process described in A225642.

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 4, 4, 4, 5, 4, 6, 5, 6, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 8, 9, 8, 8, 9, 9, 9, 9, 9, 10, 11, 10, 10, 11, 11, 10, 10, 12, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 11, 13, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14

Offset: 0

Antti Karttunen, May 15 2013

nonn

a(0)=0, as its only partition is an empty partition {}, and by convention lcm()=1, thus it takes no steps to reach from 1 to A003418(0)=1.

The records occur at positions 0, 3, 5, 9, 11, 13, 19, 27, 30, 33, 43, 44, 51, 65, 74, 82, ... and they seem to occur in order, i.e., as A001477. Thus the record-positions probably also give the left inverse function for this sequence. It also seems that each integer occurs only finite times in this sequence, so there should be a right inverse function as well.

Cf. A225644, A225633, A225639, A226055, A226056.

Scheme
```
(define (A225643 n) (-1+ (A225644 n)))
```

a(n) = A225644(n) - 1.

cp's OEIS Frontend

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

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A225629 a(n) = Last value in column n of A225630 which is not yet the fixed point A003418(n) of that column.

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Scheme

Formula

A225643 Number of steps to reach a fixed point (A003418(n)), when starting from partition {n} of n and continuing with the process described in A225642.

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Author

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Comments

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Scheme

Formula