cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A135776 Numbers having number of divisors equal to number of digits in base 6.

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%I A135776 #16 Dec 06 2018 15:29:48
%S A135776 1,7,11,13,17,19,23,29,31,49,121,169,217,218,219,221,226,235,237,247,
%T A135776 249,253,254,259,262,265,267,274,278,287,291,295,298,299,301,302,303,
%U A135776 305,309,314,319,321,323,326,327,329,334,335,339,341,343,346,355,358
%N A135776 Numbers having number of divisors equal to number of digits in base 6.
%C A135776 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 A135776 G. C. Greubel, <a href="/A135776/b135776.txt">Table of n, a(n) for n = 1..1000</a>
%H A135776 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 A135776 a(1) = 1 since 1 has 1 divisor and 1 digit (in base 6 as in any other base).
%e A135776 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 A135776 Then come the squares of primes (3 divisors) between 6^2 = 100_6 and 6^3 - 1 = 555_6.
%e A135776 These are followed by all semiprimes and cubes of primes (4 divisors) between 6^3 and 6^4 - 1.
%t A135776 Select[Range[500], DivisorSigma[0, #] == IntegerLength[#, 6] &] (* _G. C. Greubel_, Nov 08 2016 *)
%o A135776 (PARI) for(d=1,4,for(n=6^(d-1),6^d-1,d==numdiv(n)&print1(n", ")))
%Y A135776 Cf. A135772-A135779, A095862.
%K A135776 base,nonn
%O A135776 1,2
%A A135776 _M. F. Hasler_, Nov 28 2007