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Search: id:A036763
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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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14
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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
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Erdos P. and Suranyi J. (1960), Selected Topics in Number Theory. Tankonyvkiado, Budapest (In Hungarian).
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EXAMPLE
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A computer shows that the given terms do not occur as value of x/d[ x ] if x<2^22=4194304. For larger x this is impossible since if d[ x ]<Sqr[ x ], then x/d[ x ]>Sqr[ 4194304 ]=2048.
Example: No natural number x exists for which x=18*d[x].
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CROSSREFS
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Cf. A000005, A033950, A036761, A036762, A051278, A051279, A051280.
Sequence in context: A093018 A003634 A080910 this_sequence A090064 A082804 A109911
Adjacent sequences: A036760 A036761 A036762 this_sequence A036764 A036765 A036766
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
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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 ]
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