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A189394
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Highly composite numbers whose number of divisors is also highly composite.
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4
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1, 2, 6, 12, 60, 360, 1260, 2520, 5040, 55440, 277200, 720720, 3603600, 61261200, 2205403200, 293318625600, 6746328388800, 195643523275200
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OFFSET
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1,2
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COMMENTS
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Both n and d(n) are highly composite numbers.
It is extremely likely that this sequence is complete. The highly composite numbers have a very special form. The number of divisors of a large HCN has a high power of 2 in its factorization -- which is not the form of an HCN. - T. D. Noe, Apr 21 2011
All but a(7) and a(12) are a multiple of the previous term: ratios a(n+1) / a(n) are (2, 3, 2, 5, 6, 7/2, 2, 2, 11, 5, 13/5, 5, 17, 36, 133, 23, 29, ...?). - M. F. Hasler, Jun 20 2022
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LINKS
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EXAMPLE
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d(60) = 12; both 60 and 12 are highly composite numbers
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MATHEMATICA
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PROG
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M189394=[1, 2]/*for memoization*/; A189394(n)={if(#M189394<n, my(s=self()(n-2), k=self()(n-1)\/s); while(!is_A189394(k++*s), ); M189394=concat(M189394, k*s)); M189394[n]} \\ M. F. Hasler, Jun 20 2022
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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Typo in a(15) corrected by Ben Beer, Jul 20 2016
Keywords fini and full, following Øverlier's thesis, added by Michel Marcus, May 25 2023
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STATUS
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approved
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