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Search: id:A098895
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| A098895 |
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Number of divisors of the n-th superior highly composite number. |
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+0
1
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| 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
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OFFSET
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1,1
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COMMENT
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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).
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REFERENCES
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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.
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LINKS
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S. Ramanujan, Highly Composite Numbers.
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FORMULA
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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.
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EXAMPLE
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a(8)=60 because the eighth superior highly composite number, 5040, has 60 divisors.
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CROSSREFS
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Cf. A000705, A002201.
Sequence in context: A089696 A099316 A007416 this_sequence A023995 A018189 A167706
Adjacent sequences: A098892 A098893 A098894 this_sequence A098896 A098897 A098898
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KEYWORD
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nonn
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AUTHOR
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David Terr (David_C_Terr(AT)raytheon.com), Oct 14 2004
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