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A036763
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Numbers n such that x*d[n] = n has no solution for x, where d (A000005) is number of divisors; sequence gives impossible n/d[n] quotients in order of magnitude.
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15
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18, 27, 30, 45, 63, 64, 72, 99, 105, 112, 117, 144, 153, 160, 162, 165, 171, 195, 207, 225, 243, 252, 255, 261, 279, 285, 288, 294, 320, 333, 336, 345, 352, 360, 369, 387, 396, 405, 416, 423, 435, 441, 465, 468, 477, 490, 504, 531, 544, 549, 555, 567, 576
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A special case of a bound on d[ n ] by Erdos and Suranyi (1960) was used to get a limit: a=x/d[ x ]>0.5*Sqrt[ x ] and below 4194304 a computer test shows these values did not occur as x=a*d[ x ]. For larger x this is impossible since if d[ x ]<Sqr[ x ], then x/d[ x ] > Sqr[ 4194304 ]=2048 > the given terms.
A051521(a(n)) = 0. - Reinhard Zumkeller, Dec 28 2011
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REFERENCES
| Erdos P. and Suranyi J. (1960), Selected Topics in Number Theory. Tankonyvkiado, Budapest (In Hungarian).
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LINKS
| Donovan Johnson, Table of n, a(n) for n = 1..5000
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EXAMPLE
| No natural number x exists for which x=18*d[x].
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MAPLE
| with(numtheory): A036763 := proc(n) local k, p: for k from 1 to 4*n^2 do p:=n*k: if(p=n*tau(p))then return NULL: fi: od: return n: end: seq(A036763(n), n=1..100); # Nathaniel Johnston, May 04 2011
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PROG
| (Haskell)
a036763 n = a036763_list !! (n-1)
a036763_list = filter ((== 0) . a051521) [1..]
-- Reinhard Zumkeller, Dec 28 2011
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CROSSREFS
| Cf. A000005, A033950, A036761, A036762, A036764, A051278, A051279, A051280.
Sequence in context: A167336 A003634 A080910 * A186129 A151741 A090064
Adjacent sequences: A036760 A036761 A036762 * A036764 A036765 A036766
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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