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A321303
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a(n) = floor(d(n) * n^(11/2)) where d(n) is the number of divisors of n.
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1
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1, 90, 841, 6144, 13975, 76188, 88934, 370727, 531441, 1264911, 1068291, 5171875, 2677431, 8049412, 11764186, 20971520, 11708440, 48100548, 21586130, 85865010, 74862807, 96690707, 61735233, 312069853, 146484375, 242333472, 298236431, 546412244, 220911835, 1064772651, 318800733, 1138875187
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OFFSET
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1,2
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COMMENTS
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|tau(n)| <= d(n) * n^(11/2) where tau(n) is Ramanujan function. So |tau(n)| <= a(n).
Ramanujan conjectured in 1916 that |tau(p)| <= 2 * p^(11/2) for all primes p and Pierre Deligne proved this conjecture in 1974. [Wikipedia] - Bernard Schott, Oct 24 2019
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Tau Function
Wikipedia, Ramanujan tau function
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MAPLE
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f:= n -> floor(numtheory:-tau(n)*n^(11/2)):
map(f, [$1..100]); # Robert Israel, Oct 23 2019
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PROG
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(MAGMA) [Floor(NumberOfDivisors(n)*n^(11/2)): n in [1..32]]; // Marius A. Burtea, Oct 24 2019
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CROSSREFS
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Cf. A000005, A000594, A076847.
Sequence in context: A232588 A097372 A263170 * A101243 A173483 A202960
Adjacent sequences: A321300 A321301 A321302 * A321304 A321305 A321306
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Nov 03 2018
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STATUS
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approved
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