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Search: id:A135776
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| A135776 |
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Numbers having number of divisors equal to number of digits in base 6. |
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+0
1
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| 1, 7, 11, 13, 17, 19, 23, 29, 31, 49, 121, 169, 217, 218, 219, 221, 226, 235, 237, 247, 249, 253, 254, 259, 262, 265, 267, 274, 278, 287, 291, 295, 298, 299, 301, 302, 303, 305, 309, 314, 319, 321, 323, 326, 327, 329, 334, 335, 339, 341, 343, 346, 355, 358
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Since 6 is not a prime, no element > 1 of the sequence A000400(k)=6^k (having k+1 digits in base 6, but much more divisors) can be member of this sequence. However all powers of 7 up to 7^11 are in this sequence, having the same number of digits (in base 6) than the same power of 6 (since 11 = floor(log(7/6)/log(6))) and also that number of divisors (since 7 is prime).
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EXAMPLE
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a(1) = 1 since 1 has 1 divisor and 1 digit (in base 6 as in any other base).
They are followed by the primes (having 2 divisors {1,p}) between 6 and 6^2-1 (to have 2 digits in base 6).
Then come the squares of primes (3 divisors) between 6^2=100[6] and 6^3-1=555[6].
These are followed by all semiprimes and cubes of primes (4 divisors) between 6^3 and 6^4-1.
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PROGRAM
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(PARI) for(d=1, 4, for(n=6^(d-1), 6^d-1, d==numdiv(n)&print1(n", ")))
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CROSSREFS
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Cf. A135772-A135779, A095862.
Sequence in context: A078873 A020603 A163648 this_sequence A067831 A086998 A028416
Adjacent sequences: A135773 A135774 A135775 this_sequence A135777 A135778 A135779
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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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