

A135776


Numbers having number of divisors equal to number of digits in base 6.


1



1, 7, 11, 13, 17, 19, 23, 29, 31, 49, 121, 169, 217, 218, 219, 221, 226, 235, 237, 247, 249, 253, 254, 259, 262, 265, 267, 274, 278, 287, 291, 295, 298, 299, 301, 302, 303, 305, 309, 314, 319, 321, 323, 326, 327, 329, 334, 335, 339, 341, 343, 346, 355, 358
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OFFSET

1,2


COMMENTS

Since 6 is not a prime, no element > 1 of the sequence A000400(k)=6^k (having k+1 digits in base 6, but much more divisors) can be a member of this sequence. However, all powers of 7 up to 7^11 are in this sequence, having the same number of digits (in base 6) as the same power of 6 (since 11 = floor(log(7/6)/log(6))) and also that number of divisors (since 7 is prime).


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000
Abel Jansma, E_8 Symmetry Structures in the Ising model, Master's thesis, University of Amsterdam, 2018.


EXAMPLE

a(1) = 1 since 1 has 1 divisor and 1 digit (in base 6 as in any other base).
They are followed by the primes (having 2 divisors {1,p}) between 6 and 6^2  1 (to have 2 digits in base 6).
Then come the squares of primes (3 divisors) between 6^2 = 100_6 and 6^3  1 = 555_6.
These are followed by all semiprimes and cubes of primes (4 divisors) between 6^3 and 6^4  1.


MATHEMATICA

Select[Range[500], DivisorSigma[0, #] == IntegerLength[#, 6] &] (* G. C. Greubel, Nov 08 2016 *)


PROG

(PARI) for(d=1, 4, for(n=6^(d1), 6^d1, d==numdiv(n)&print1(n", ")))


CROSSREFS

Cf. A135772A135779, A095862.
Sequence in context: A020603 A283532 A163648 * A067831 A086998 A028416
Adjacent sequences: A135773 A135774 A135775 * A135777 A135778 A135779


KEYWORD

base,nonn


AUTHOR

M. F. Hasler, Nov 28 2007


STATUS

approved



