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A166735
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Superabundant numbers (A004394) that are not highly composite (A002182).
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3
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1163962800, 4658179125600, 13974537376800, 144403552893600, 433210658680800, 10685862914126400, 21371725828252800, 32057588742379200, 37400520199442400, 64115177484758400, 1533421328177138400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Alaoglu and Erdos mention the first term in footnote 14.
Because the "shapes" of superabundant and highly composite numbers are different, there is a last superabundant number that is also highly composite. In factored form, that 154-digit number is N = A004394(1023) = A002182(2567) = 2^10 3^6 5^4 7^3 11^3 13^2 17^2 19^2 23^2 29 31 37...347. In other words, this sequence contains all superabundant numbers greater than N. [From T. D. Noe (noe(AT)sspectra.com), Oct 26 2009]
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REFERENCES
| L. Alaoglu and P. Erdos, On highly composite and similar numbers, Trans. Amer. Math. Soc., 56 (1944), 448-469.
S. Ramanujan, Highly composite numbers, Annotated and with a foreword by J.-L. Nicholas and G. Robin, Ramanujan J., 1 (1997), 119-153.
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FORMULA
| a(574+i) = A004394(1023+i) for i>0.
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CROSSREFS
| A166981 (intersection of SA and HC numbers) [From T. D. Noe (noe(AT)sspectra.com), Oct 26 2009]
Cf. A189228 (SA numbers that are not CA).
Sequence in context: A158707 A159568 A115173 * A104933 A119333 A195988
Adjacent sequences: A166732 A166733 A166734 * A166736 A166737 A166738
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Oct 20 2009
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