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A242421 Fixed points of A153212: After a(1) = 1, numbers of the form p_i1^i1 * p_i2^(i2-i1) * p_i3^(i3-i2) * ... * p_ik^(ik-i_{k-1}), where p_i's are distinct primes present in the prime factorization of n, with i1 < i2 < i3 < ... < ik, and k = A001221(n) and ik = A061395(n). 5
1, 2, 6, 9, 30, 45, 50, 125, 210, 294, 315, 350, 441, 686, 875, 2310, 2401, 3234, 3465, 3630, 3850, 4851, 5445, 6050, 7546, 7986, 9625, 11979, 15125, 26411, 29282, 30030, 35490, 42042, 45045, 47190, 49686, 50050, 53235, 59150, 63063, 65910, 70785, 74529, 78650, 98098, 98865, 103818, 109850, 115934, 125125, 147875, 155727, 161051, 171366, 196625, 257049, 274625, 343343, 380666, 405769, 510510 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is closed with respect to A122111, i.e., for any n, A122111(a(n)) is either the same as a(n) or some other term a(k) of the sequence.

These numbers encode partitions in whose Young diagrams all pairs of successive horizontal and vertical segments (those pairs sharing "a common convex corner") are of equal length. Cf. the example-illustration at A153212.

Note: The seventh primorial, 510510 (= A002110(7)) occurs here as a term a(62).

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

2 = p_1^1 is present, as the first prime index delta and exponent are equal.

3 = p_2^1 is not present, as 1 <> 2.

6 = p_1^1 * p_2^(2-1) is present.

9 = p_2^2 is present, as 2 = 2.

30 = p_1^1 * p_2^(2-1) * p_3^(3-2) is present, as all primorials are.

50 = p_1^1 * p_3^(3-1) is present also.

PROG

(Scheme, with Antti Karttunen's IntSeq-library)

(define A242421 (FIXED-POINTS 1 1 A153212)) ;; Very slow, but gives the terms in order.

;; The following is a faster version, but gives the terms in non-monotone order. Note that its indexing starts from zero.

;; A000975 gives the positions where primorials occur, after which only larger terms occur, use this fact for selecting a prefix sequence of appropriate length before sorting.

;; E.g. (A242421_in_wrong_order 85) = 510510 = (A242421_in_wrong_order (A006068 127))

(define (A242421_in_wrong_order n) (let ((complist (binexp->runcount1list n))) (apply * (map (lambda (i e) (expt (A000040 i) e)) (partsums complist) complist))))

;; For the function binexp->runcount1list and partsums, see for example A129594.

CROSSREFS

Subsequences: A002110 (primorial numbers), A062457.

Cf. A242422, A088902, A241912, A209861, A209636, A129594.

Sequence in context: A121624 A103019 A101823 * A093397 A082459 A129831

Adjacent sequences:  A242418 A242419 A242420 * A242422 A242423 A242424

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 16 2014

STATUS

approved

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Last modified January 18 01:36 EST 2019. Contains 319260 sequences. (Running on oeis4.)