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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 (list; graph; refs; listen; history; text; internal format)
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^(d-1), 6^d-1, d==numdiv(n)&print1(n", ")))

CROSSREFS

Cf. A135772-A135779, 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

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)