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A098895 Number of divisors of the n-th superior highly composite number. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 30 16:16 EDT 2020. Contains 333127 sequences. (Running on oeis4.)