A135778 Numbers having number of divisors equal to number of digits in base 8.

1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 121, 169, 289, 361, 514, 515, 517, 519, 526, 527, 533, 535, 537, 538, 542, 543, 545, 551, 553, 554, 559, 562, 565, 566, 573, 579, 581, 583, 586, 589, 591, 597, 611, 614, 622, 623, 626, 629, 633, 634

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

Cf. A135772-A135779, A095862.

Sequence in context: A268031 A167847 A135779 * A078875 A244555 A052293

Adjacent sequences: A135775 A135776 A135777 * A135779 A135780 A135781

Keyword

base,nonn

Author

M. F. Hasler, Nov 28 2007

Extensions

More terms from Harvey P. Dale, Mar 04 2016

Status

approved