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A166981 Superabundant numbers (A004394) that are highly composite (A002182). 12
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
From Michael De Vlieger, Dec 29 2020: (Start)
All terms are products of primorials (numbers in A002110), thus, all terms are also in A025487, itself a subsequence of A055932.
Since the colossally abundant numbers (CA, A004490) are also superabundant, and since the superior highly composite (SHC A002201) numbers are also highly composite, the finite sequence A224078 containing numbers both CA and SHC is a subsequence of this sequence. Likewise, A304234 (numbers that are SA, HC, & SHC but not CA) and A304235 (numbers that are SA, HC, & CA but not SHC), and A338786 (SA and HC, but neither CA nor SHC) are mutually exclusive finite subsequences of this sequence. (End)
LINKS
T. D. Noe, Table of n, a(n) for n = 1..449 (complete sequence)
Michael De Vlieger, Annotated plot of a(n) at (x,y) = (a(n)/P), P) where P = A002110(A001221(a(n)) showing all 449 terms.
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. 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. A002110, A002182, A004394, A025487, A055932, A166735 (SA numbers that are not HC numbers), A224078, A304234, A304235, A308913, A338786.
Sequence in context: A002182 A340840 A077006 * A004394 A189686 A355304
KEYWORD
fini,full,nonn
AUTHOR
T. D. Noe, Oct 26 2009
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)