

A189394


Highly composite numbers whose number of divisors is also highly composite.


4



1, 2, 6, 12, 60, 360, 1260, 2520, 5040, 55440, 277200, 720720, 3603600, 61261200, 2205403200, 293318625600, 6746328388800, 195643523275200
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OFFSET

1,2


COMMENTS

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


LINKS



EXAMPLE

d(60) = 12; both 60 and 12 are highly composite numbers


MATHEMATICA



PROG

M189394=[1, 2]/*for memoization*/; A189394(n)={if(#M189394<n, my(s=self()(n2), k=self()(n1)\/s); while(!is_A189394(k++*s), ); M189394=concat(M189394, k*s)); M189394[n]} \\ M. F. Hasler, Jun 20 2022


CROSSREFS



KEYWORD

nonn,fini,full


AUTHOR



EXTENSIONS

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


STATUS

approved



