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.

A135775 Numbers having number of divisors equal to number of digits in base 5.

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%I A135775 #12 Nov 09 2016 00:48:55
%S A135775 1,5,7,11,13,17,19,23,25,49,121,125,129,133,134,141,142,143,145,146,
%T A135775 155,158,159,161,166,177,178,183,185,187,194,201,202,203,205,206,209,
%U A135775 213,214,215,217,218,219,221,226,235,237,247,249,253,254,259,262,265,267
%N A135775 Numbers having number of divisors equal to number of digits in base 5.
%C A135775 Since 5 is a prime, any power 5^k has k+1 divisors { 5^i ; i=0..k } and the same number of digits in base 5; thus the sequence A000351(k)=5^k is a subsequence of this one. It also includes the powers of 7 up to 7^4, since (7/5)^4 < 5 < (7/5)^5.
%H A135775 G. C. Greubel, <a href="/A135775/b135775.txt">Table of n, a(n) for n = 1..1000</a>
%e A135775 a(1) = 1 since 1 has 1 divisor and 1 digit (in base 5).
%e A135775 2,3,4 have 2 resp. 3 divisors but only 1 digit in base 5, so they are not members of the sequence.
%e A135775 a(2) = 5 = 10_5 has 2 divisors { 1, 5 } and 2 digits in base 5, so it is (the second term) in this sequence.
%t A135775 Select[Range[300],DivisorSigma[0,#]==IntegerLength[#,5]&] (* _Harvey P. Dale_, Mar 14 2013 *)
%o A135775 (PARI) for(d=1,4,for(n=5^(d-1),5^d-1,d==numdiv(n)&print1(n", ")))
%Y A135775 Cf. A135772-A135779, A095862.
%K A135775 base,nonn
%O A135775 1,2
%A A135775 _M. F. Hasler_, Nov 28 2007