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.
%I A278835 #17 Jul 08 2023 20:57:32 %S A278835 3,3,11,17,41,73,101,137,251,257,271,353,401,449,641,751,1201,1409, %T A278835 1601,3541,4001,4801,5051,9091,10753,15361,16001,19841,21001,21401, %U A278835 24001,25601,27961,37501,40961,43201,60101,62501,65537,69857,76001,76801,160001,162251,163841,307201,453377,524801,544001,670001,952001,976193,980801 %N A278835 Prime factors (counting multiplicity) of 10^10^10^10^2 - 1. %C A278835 From _Jon E. Schoenfield_, Dec 02 2016, paraphrasing information from the Munafo link: (Start) %C A278835 The decimal expansion of 10^10^10^10^2 - 1 would be 1 googolplex digits long, with each digit a 9. Many factors of this number can be identified using simple facts of modular arithmetic. %C A278835 Since its digits are all 9's, it is divisible by 9=3*3. Since its digits are all 9's and the number of digits is even, it is divisible by 99 (as are 9999=99*101, 999999=99*10101, 99999999=99*1010101, etc.), and thus divisible by 11. %C A278835 By the same principle, it is divisible by 9999, 99999, 99999999, and by any other number whose decimal expansion consists of k 9's where k is of the form 2^a * 5^b, where a and b are nonnegative integers up to 10^100 (see A003592) and all their divisors. Additional factors can be found using Fermat's Little Theorem. %C A278835 Consequently, a large number of factors of 10^10^10^10^2 - 1 are known. (End) %H A278835 Robert G. Wilson v, <a href="/A278835/b278835.txt">Table of n, a(n) for n = 1..587</a> %H A278835 Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/glpxm1.pl">Known prime factors of Googolduplex - 1</a> %H A278835 Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/glpxm1.pl?digits=1"> Known 1-digit prime factors of Googolduplex - 1</a> %H A278835 Robert P. Munafo, <a href="http://mrob.com/pub/math/numbers-22.html#lp2_e008_37"> Notable Properties of Specific Numbers</a> %e A278835 10^10^10^10^2 - 1 = 10^10^10^100 - 1 = 999...999 (a total of a googolplex of nines). %Y A278835 Cf. A227246. %K A278835 nonn,fini %O A278835 1,1 %A A278835 _Robert Munafo_ and _Robert G. Wilson v_, Nov 28 2016