1,2

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).

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.

(PARI) for(d=1, 4, for(n=8^(d-1), 8^d-1, d==numdiv(n)&print1(n", ")))

Cf. A135772-A135779, A095862.

Sequence in context: A125845 A108871 A135779 this_sequence A078875 A052293 A038842

Adjacent sequences: A135775 A135776 A135777 this_sequence A135779 A135780 A135781

base,nonn

M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 28 2007