OFFSET
1,2
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 fewer 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).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
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.
MATHEMATICA
Select[Range[1000], IntegerLength[#, 8]==DivisorSigma[0, #]&] (* Harvey P. Dale, Mar 04 2016 *)
PROG
(PARI) for(d=1, 4, for(n=8^(d-1), 8^d-1, d==numdiv(n)&print1(n", ")))
CROSSREFS
KEYWORD
base,nonn
AUTHOR
M. F. Hasler, Nov 28 2007
EXTENSIONS
More terms from Harvey P. Dale, Mar 04 2016
STATUS
approved