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Search: id:A135774
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| A135774 |
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Numbers having number of divisors equal to number of digits in base 4. |
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+0
1
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| 1, 5, 7, 11, 13, 25, 49, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205, 206, 209, 213, 214, 215, 217, 218
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Since 4 is not a prime, no element > 1 of the sequence A000302(k)=4^k (having k+1 digits in base 4 but 2k+1 divisors) can be member of this sequence. However all powers of 5 up to 5^6 are in this sequence, having the same number of digits (in base 4) than the same power of 4 (since (5/4)^6 < 4 < (5/4)^7), and also that number of divisors.
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EXAMPLE
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a(1) = 1 since 1 has 1 divisor and 1 digit (in base 4 as in any other base).
a(2)..a(5) = 5,7,11,13 are the primes (to have 2 divisors {1,p}) between 4 and 4^2-1 (to have 2 digits in base 4).
a(6),a(7) = 25,49 are the squares of primes (3 divisors) between 4^2=100[4] and 4^3-1=333[4].
They are followed by all semiprimes and cubes of primes (4 divisors) between 4^3 and 4^4-1.
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PROGRAM
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(PARI) for(d=1, 4, for(n=4^(d-1), 4^d-1, d==numdiv(n)&print1(n", ")))
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CROSSREFS
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Cf. A135772-A135779, A095862.
Adjacent sequences: A135771 A135772 A135773 this_sequence A135775 A135776 A135777
Sequence in context: A050541 A098865 A022885 this_sequence A135930 A136055 A073340
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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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