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Search: id:A135773
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| A135773 |
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Numbers having number of divisors equal to number of digits in base 3. |
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+0
2
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| 1, 3, 5, 7, 9, 25, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 81, 243, 244, 245, 261, 268, 275, 279, 284, 292, 316, 325, 332, 333, 338, 356, 363, 369, 387, 388, 404, 412, 423, 425, 428, 436, 452, 475, 477, 507, 508, 524, 531, 539, 548, 549
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Since 3 is a prime, any power 3^k has k+1 divisors { 3^i ; i=0..k } and the same number of digits in base 3; thus the sequence A000244(k)=3^k is a subsequence of this one. Note that no number in between 3^4 and 3^5, neither in between 3^6 and 3^7, is in this sequence.
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EXAMPLE
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a(1) = 1 since 1 has 1 divisor and 1 digit (in base 3).
2 has 2 divisors but only 1 digit in base 3, so it is not member of the sequence.
a(2)..a(4) = 3,5,7 all have 2 divisors and 2 digits in base 3.
81 = 3^4 = 10000[3] is the only number with 5 divisors and 5 digits in base 3, so it is followed by 243 = 3^5 = 100000[3].
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PROGRAM
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(PARI) for(d=1, 6, for(n=3^(d-1), 3^d-1, d==numdiv(n)&print1(n", ")))
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CROSSREFS
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Cf. A135772-A135779, A095862.
Adjacent sequences: A135770 A135771 A135772 this_sequence A135774 A135775 A135776
Sequence in context: A099995 A100028 A053681 this_sequence A131668 A119252 A141708
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KEYWORD
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base,nonn
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AUTHOR
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 28 2007
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