

A166981


Superabundant numbers (A004394) that are highly composite (A002182).


8



1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 665280, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 8648640, 10810800
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OFFSET

1,2


COMMENTS

The intersection of superabundant and highly composite numbers has exactly 449 terms, the largest of which is 2^10 3^6 5^4 7^3 11^3 13^2 17^2 19^2 23^2 29 31 37...347.
The argument showing that this is a finite sequence seems to be given in A166735.  N. J. A. Sloane, Jan 04 2019
Pillai proved that this sequence is finite and asked for its number of terms (he used the term "highly abundant" for superabundant numbers).  Amiram Eldar, Jun 30 2019


LINKS

T. D. Noe, Table of n, a(n) for n=1..449 (complete sequence)
Thomas Fink, Recursively divisible numbers, arXiv:1912.07979 [math.NT], 2019. Mentions this sequence.
S. Sivasankaranarayana Pillai, Highly abundant numbers, Bulletin of the Calcutta Mathematical Society, Vol. 35, No. 1 (1943), pp. 141156.
S. Sivasankaranarayana Pillai, On numbers analogous to highly composite numbers of Ramanujan, Rajah Sir Annamalai Chettiar Commemoration Volume, ed. Dr. B. V. Narayanaswamy Naidu, Annamalai University, 1941, pp. 697704.


CROSSREFS

Cf. A166735 (SA numbers that are not HC numbers).
Sequence in context: A242298 A002182 A077006 * A004394 A189686 A137425
Adjacent sequences: A166978 A166979 A166980 * A166982 A166983 A166984


KEYWORD

fini,full,nonn


AUTHOR

T. D. Noe, Oct 26 2009


STATUS

approved



