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

1,1

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).

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.

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.

Example

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

Crossrefs

Cf. A000705, A002201.

Sequence in context: A099316 A007416 A293132 * A266543 A330711 A220219

Adjacent sequences: A098892 A098893 A098894 * A098896 A098897 A098898

Keyword

nonn

Author

David Terr, Oct 14 2004

Status

approved