

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
Thomas Fink, Recursively divisible numbers, arXiv:1912.07979 [math.NT], 2019. Mentions this sequence.
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



