

A166735


Superabundant numbers (A004394) that are not highly composite (A002182).


6



1163962800, 4658179125600, 13974537376800, 144403552893600, 433210658680800, 10685862914126400, 21371725828252800, 32057588742379200, 37400520199442400, 64115177484758400, 1533421328177138400
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OFFSET

1,1


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 154digit 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.  T. D. Noe, Oct 26 2009


LINKS

T. D. Noe, Table of n, a(n) for n = 1..574
L. Alaoglu and P. Erdos, On highly composite and similar numbers, Trans. Amer. Math. Soc., 56 (1944), 448469. Errata
S. Ramanujan, Highly composite numbers, Proceedings of the London Mathematical Society, 2, XIV, 1915, 347  409.
S. Ramanujan, Highly composite numbers, Annotated and with a foreword by J.L. Nicolas and G. Robin, Ramanujan J., 1 (1997), 119153.


FORMULA

a(574+i) = A004394(1023+i) for i>0.


CROSSREFS

Cf. A166981 (intersection of SA and HC numbers).  T. D. Noe, Oct 26 2009
Cf. A189228 (SA numbers that are not CA).
Sequence in context: A159568 A287547 A115173 * A104933 A119333 A309227
Adjacent sequences: A166732 A166733 A166734 * A166736 A166737 A166738


KEYWORD

nonn


AUTHOR

T. D. Noe, Oct 20 2009


STATUS

approved



