A098895 Number of divisors of the n-th superior highly composite number.

2, 4, 6, 12, 16, 24, 48, 60, 120, 240, 288, 384, 576, 1152, 2304, 2688, 5376, 8064, 16128, 20160, 40320, 46080, 92160, 184320, 368640, 737280, 983040, 1966080, 3932160, 4423680, 6635520, 13271040, 15925248, 31850496, 63700992, 127401984

Offset: 1

Author

David Terr, Oct 14 2004

Keywords

• nonn

Comments

Sequence A002201 gives the values of the n-th superior highly composite number N(n) and A000705 gives the values of the (prime) ratio N(n)/N(n-1).

Examples

			a(8)=60 because the eighth superior highly composite number, 5040, has 60 divisors.
		

References

• S. Ramanujan, Highly composite numbers, Proc. London Math. Soc., 14 (1915), 347-407. Reprinted in Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962, pp. 78-129. See esp. pp. 87, 115.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3401 (calculated using the b-file at A000705)
• S. Ramanujan, Highly Composite Numbers.

Crossrefs

Cf. A000705, A002201.

Formula

a(n) = a(n-1) * (1 + 1/k(n)), where k(n) is the p(n)-adic valuation of the n-th superior highly composite number N(n), with p(n) = N(n)/N(n-1) and N(0)=1.