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%I #13 Nov 09 2016 02:35:00
%S 1,11,13,17,19,23,29,31,37,41,43,47,53,59,61,121,169,289,361,514,515,
%T 517,519,526,527,533,535,537,538,542,543,545,551,553,554,559,562,565,
%U 566,573,579,581,583,586,589,591,597,611,614,622,623,626,629,633,634
%N Numbers having number of divisors equal to number of digits in base 8.
%C 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).
%H Harvey P. Dale, <a href="/A135778/b135778.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1) = 1 since 1 has 1 divisor and 1 digit (in base 8 as in any other base).
%e They are followed by the primes (having 2 divisors {1,p}) between 8 and 8^2 - 1 (to have 2 digits in base 8).
%e Then come the squares of primes (3 divisors) between 8^2 = 100_8 and 8^3 - 1 = 777_8.
%e These are followed by all semiprimes and cubes of primes (4 divisors) between 8^3 and 8^4 - 1.
%t Select[Range[1000],IntegerLength[#,8]==DivisorSigma[0,#]&] (* _Harvey P. Dale_, Mar 04 2016 *)
%o (PARI) for(d=1,4,for(n=8^(d-1),8^d-1,d==numdiv(n)&print1(n", ")))
%Y Cf. A135772-A135779, A095862.
%K base,nonn
%O 1,2
%A _M. F. Hasler_, Nov 28 2007
%E More terms from _Harvey P. Dale_, Mar 04 2016
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