

A189394


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


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

Table of n, a(n) for n=1..18.
A. Flammenkamp, Highly composite numbers


EXAMPLE

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


MATHEMATICA

(* First run program at A002182 *) Select[A002182, MemberQ[A002182, DivisorSigma[0, #]] &] (* Alonso del Arte, Apr 21 2011 *)


PROG

(PARI) From M. F. Hasler, Jun 20 2022: (Start)
is_A189394(n)={is_A002182(numdiv(n)) && is_A002182(n)}
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]} \\ (End)


CROSSREFS

Cf. A002182, A002183, A141320.
Sequence in context: A309875 A254232 A335831 * A182862 A072938 A160274
Adjacent sequences: A189391 A189392 A189393 * A189395 A189396 A189397


KEYWORD

nonn,more


AUTHOR

Krzysztof Ostrowski, Apr 21 2011


EXTENSIONS

Typo in a(15) corrected by Ben Beer, Jul 20 2016


STATUS

approved



