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A135778
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Numbers having number of divisors equal to number of digits in base 8.
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1
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1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 121, 169, 289, 361
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Since 8 is not a prime, no element > 1 of the sequence A001018(k)=8^k (having k+1 digits in base 8, but much more divisors) can be member of this sequence. Also, no power of a prime less than 8 can be in the sequence, since it will always have less divisors than digits in base 8. However all powers of 11 up to 11^6 are in this sequence, having the same number of digits (in base 8) than the same power of 8 (since 6 = floor(log(11/8)/log(8))) and also that number of divisors (since 11 is prime).
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EXAMPLE
| a(1) = 1 since 1 has 1 divisor and 1 digit (in base 8 as in any other base).
They are followed by the primes (having 2 divisors {1,p}) between 8 and 8^2-1 (to have 2 digits in base 8).
Then come the squares of primes (3 divisors) between 8^2=100[8] and 8^3-1=777[8].
These are followed by all semiprimes and cubes of primes (4 divisors) between 8^3 and 8^4-1.
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PROG
| (PARI) for(d=1, 4, for(n=8^(d-1), 8^d-1, d==numdiv(n)&print1(n", ")))
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CROSSREFS
| Cf. A135772-A135779, A095862.
Sequence in context: A108871 A167847 A135779 * A078875 A052293 A038842
Adjacent sequences: A135775 A135776 A135777 * A135779 A135780 A135781
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KEYWORD
| base,nonn
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AUTHOR
| M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 28 2007
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