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A135778 Numbers having number of divisors equal to number of digits in base 8. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 18 05:48 EST 2018. Contains 299298 sequences. (Running on oeis4.)