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 A135774 Numbers having number of divisors equal to number of digits in base 4. 1
 1, 5, 7, 11, 13, 25, 49, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205, 206, 209, 213, 214, 215, 217, 218 (list; graph; refs; listen; history; text; internal format)
 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 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, 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 Cf. A135772-A135779, A095862. Sequence in context: A263467 A200143 A265780 * A180946 A265006 A135930 Adjacent sequences:  A135771 A135772 A135773 * A135775 A135776 A135777 KEYWORD base,nonn AUTHOR M. F. Hasler, Nov 28 2007 STATUS approved

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Last modified May 9 05:11 EDT 2021. Contains 343688 sequences. (Running on oeis4.)