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%I #16 Dec 06 2018 15:29:48
%S 1,7,11,13,17,19,23,29,31,49,121,169,217,218,219,221,226,235,237,247,
%T 249,253,254,259,262,265,267,274,278,287,291,295,298,299,301,302,303,
%U 305,309,314,319,321,323,326,327,329,334,335,339,341,343,346,355,358
%N Numbers having number of divisors equal to number of digits in base 6.
%C 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).
%H G. C. Greubel, <a href="/A135776/b135776.txt">Table of n, a(n) for n = 1..1000</a>
%H Abel Jansma, <a href="https://esc.fnwi.uva.nl/thesis/centraal/files/f1541951402.pdf">E_8 Symmetry Structures in the Ising model</a>, Master's thesis, University of Amsterdam, 2018.
%e a(1) = 1 since 1 has 1 divisor and 1 digit (in base 6 as in any other base).
%e They are followed by the primes (having 2 divisors {1,p}) between 6 and 6^2 - 1 (to have 2 digits in base 6).
%e Then come the squares of primes (3 divisors) between 6^2 = 100_6 and 6^3 - 1 = 555_6.
%e These are followed by all semiprimes and cubes of primes (4 divisors) between 6^3 and 6^4 - 1.
%t Select[Range[500], DivisorSigma[0, #] == IntegerLength[#, 6] &] (* _G. C. Greubel_, Nov 08 2016 *)
%o (PARI) for(d=1,4,for(n=6^(d-1),6^d-1,d==numdiv(n)&print1(n", ")))
%Y Cf. A135772-A135779, A095862.
%K base,nonn
%O 1,2
%A _M. F. Hasler_, Nov 28 2007
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