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A321303 a(n) = floor(d(n) * n^(11/2)) where d(n) is the number of divisors of n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

|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

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Tau Function

Wikipedia, Ramanujan tau function

MAPLE

f:= n -> floor(numtheory:-tau(n)*n^(11/2)):

map(f, [$1..100]); # Robert Israel, Oct 23 2019

PROG

(MAGMA) [Floor(NumberOfDivisors(n)*n^(11/2)): n in [1..32]]; // Marius A. Burtea, Oct 24 2019

CROSSREFS

Cf. A000005, A000594, A076847.

Sequence in context: A232588 A097372 A263170 * A101243 A173483 A202960

Adjacent sequences:  A321300 A321301 A321302 * A321304 A321305 A321306

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 03 2018

STATUS

approved

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Last modified July 5 14:18 EDT 2022. Contains 355099 sequences. (Running on oeis4.)