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A135777 Numbers having number of divisors equal to number of digits in base 7. 1

%I

%S 1,7,11,13,17,19,23,29,31,37,41,43,47,49,121,169,289,343,346,355,358,

%T 362,365,371,377,381,382,386,391,393,394,395,398,403,407,411,413,415,

%U 417,422,427,437,445,446,447,451,453,454,458,466,469,471,473,478,481

%N Numbers having number of divisors equal to number of digits in base 7.

%C Since 7 is a prime, any power 7^k has k+1 divisors { 7^i ; i=0..k } and the same number of digits in base 7; thus the sequence A000420(k)=7^k is a subsequence of this one.

%H G. C. Greubel, <a href="/A135777/b135777.txt">Table of n, a(n) for n = 1..1250</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 7 as in any other base).

%e All other numbers have at least 2 divisors so there are no other members of the sequence below a(2) = 7 = 10_7 having 2 divisors { 1, 7 } and 2 digits in base 7.

%t Select[Range[500],DivisorSigma[0,#]==IntegerLength[#,7]&] (* _Harvey P. Dale_, Feb 14 2015 *)

%o (PARI) for(d=1,4,for(n=7^(d-1),7^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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Last modified May 15 04:03 EDT 2021. Contains 343909 sequences. (Running on oeis4.)