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%I #16 Jun 08 2014 08:58:14
%S 1,2,6,9,30,45,50,125,210,294,315,350,441,686,875,2310,2401,3234,3465,
%T 3630,3850,4851,5445,6050,7546,7986,9625,11979,15125,26411,29282,
%U 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
%N 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).
%C 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.
%C 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.
%C Note: The seventh primorial, 510510 (= A002110(7)) occurs here as a term a(62).
%e 2 = p_1^1 is present, as the first prime index delta and exponent are equal.
%e 3 = p_2^1 is not present, as 1 <> 2.
%e 6 = p_1^1 * p_2^(2-1) is present.
%e 9 = p_2^2 is present, as 2 = 2.
%e 30 = p_1^1 * p_2^(2-1) * p_3^(3-2) is present, as all primorials are.
%e 50 = p_1^1 * p_3^(3-1) is present also.
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A242421 (FIXED-POINTS 1 1 A153212)) ;; Very slow, but gives the terms in order.
%o ;; The following is a faster version, but gives the terms in non-monotone order. Note that its indexing starts from zero.
%o ;; 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.
%o ;; E.g. (A242421_in_wrong_order 85) = 510510 = (A242421_in_wrong_order (A006068 127))
%o (define (A242421_in_wrong_order n) (let ((complist (binexp->runcount1list n))) (apply * (map (lambda (i e) (expt (A000040 i) e)) (partsums complist) complist))))
%o ;; For the function binexp->runcount1list and partsums, see for example A129594.
%Y Subsequences: A002110 (primorial numbers), A062457.
%Y Cf. A242422, A088902, A241912, A209861, A209636, A129594.
%K nonn
%O 1,2
%A _Antti Karttunen_, May 16 2014
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