OFFSET
1,2
COMMENTS
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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
EXAMPLE
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.
MATHEMATICA
Select[Range[500], DivisorSigma[0, #] == IntegerLength[#, 4] &] (* G. C. Greubel, Nov 08 2016 *)
PROG
(PARI) for(d=1, 4, for(n=4^(d-1), 4^d-1, d==numdiv(n)&print1(n", ")))
CROSSREFS
KEYWORD
base,nonn
AUTHOR
M. F. Hasler, Nov 28 2007
STATUS
approved