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A166981 Superabundant numbers (A004394) that are highly composite (A002182). 7
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 (list; graph; refs; listen; history; text; internal format)
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)

S. Sivasankaranarayana Pillai, Highly abundant numbers, Bulletin of the Calcutta Mathematical Society, Vol. 35,  No. 1 (1943), pp. 141-156.

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. 697-704.

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

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Last modified August 23 14:32 EDT 2019. Contains 326247 sequences. (Running on oeis4.)