A166735 Superabundant numbers (A004394) that are not highly composite (A002182).

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

Offset: 1

Author

T. D. Noe, Oct 20 2009

Keywords

• nonn

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. - 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), 448-469. 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), 119-153.

Crossrefs

Cf. A166981 (intersection of SA and HC numbers). - T. D. Noe, Oct 26 2009

Cf. A189228 (SA numbers that are not CA).

Formula

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