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 A104659 #28 Jul 08 2023 13:45:31 %S A104659 1,2,1,2,2,2,2,4,2,1,5,3,2,6,3,3,3,3,2,4,4,4,4,4,4,5,1,2,6,4,4,6,4,4, %T A104659 4,5,4,8,4,4,7,3,2,7,3,7,4,6,3,4,6,2,6,1,4,7,2,5,4,4,4,6,4,2,3,6,3,5, %U A104659 4,3,11,5,4,4,5,7,3,4,3,5,4,4,3,3,6,8,3,4,4,2,6,6,1,7,8,4,4,7,4,6,6,4,4,5,6 %N A104659 Number of distinct prime divisors of 44...441 (with n 4s). %C A104659 There are very few primes in this sequence. 41 appears as the smallest prime divisor frequently. There are many semiprimes. %C A104659 41 is prime. %C A104659 4441 is prime. %C A104659 44444 444441 is prime. %C A104659 4444 444444 444444 444444 444441 is prime. %C A104659 4444444444444444444444444444444444444444444444444444441 is prime. %C A104659 Computed using www.alpertron.com.ar/ECM.HTM %H A104659 Amiram Eldar, <a href="/A104659/b104659.txt">Table of n, a(n) for n = 1..199</a> %H A104659 Dario Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a> %H A104659 Makoto Kamada, <a href="https://stdkmd.net/nrr/4/44441.htm">Factorizations of 44...441</a>. %F A104659 a(n) = A001221(A173768(n+1)). - _Amiram Eldar_, Jan 24 2020 %e A104659 The number of distinct prime divisors of 441 is 2. %e A104659 The number of distinct prime divisors of 44444444444444444444444444444441 is four. %t A104659 f[n_] := Length@ FactorInteger[(4*10^(n + 1) - 31)/9]; Array[f, 105] (* _Robert G. Wilson v_, Aug 09 2010 *) %t A104659 PrimeNu/@Rest[FromDigits/@Table[PadLeft[{1},n,4],{n,110}]] (* _Harvey P. Dale_, Mar 16 2012 *) %Y A104659 Cf. A001221, A104564, A104517, A104484, A173768. %K A104659 nonn,base %O A104659 1,2 %A A104659 _Parthasarathy Nambi_, Apr 21 2005, extended Aug 08 2010 %E A104659 a(32) - a(105) from _Robert G. Wilson v_, Aug 09 2010