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 A376504 #11 Sep 28 2024 12:58:23 %S A376504 0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,1,0,1,0,1,0,4,0,0,1,1, %T A376504 1,1,0,1,1,1,0,4,0,1,1,1,0,1,0,1,1,1,0,1,1,1,1,1,0,4,0,1,1,0,1,4,0,1, %U A376504 1,4,0,1,0,1,1,1,1,4,0,1,0,1,0,4,1,1,1 %N A376504 Number of divisors of n that are both composite and squarefree. %C A376504 Also number of composite and squarefree m <= n such that rad(m) | n, i.e., in row n of A162306, where rad = A007947. %C A376504 This sequence is distinct from A327517; A327517(210) != a(210). %C A376504 Record setters are primorials, a(6) = 1, a(30) = 4, a(210) = 11, etc., since primorials P(n) = A002110(n) are the smallest instance of omega(n) = A001221(n). %H A376504 Michael De Vlieger, <a href="/A376504/b376504.txt">Table of n, a(n) for n = 1..10000</a> %H A376504 Michael De Vlieger, <a href="/A376504/a376504.png">Hasse diagram of row 1440 of A162306</a> showing 4 squarefree composites in green, 3 primes in red, the empty product in gray, 17 perfect powers of primes in yellow, and 72 numbers that are neither squarefree nor prime powers in blue and purple, with purple additionally representing powerful numbers that are not prime powers. %F A376504 a(n) = 2^omega(n) - omega(n) - 1 = A034444(n) - A001221(n) - 1. %F A376504 a(n) = 0 for n = p^m, where p is prime and m >= 0, i.e., n in A000961. %F A376504 a(n) = A000295(omega(n)) = A000295(A001221(n)). %t A376504 Array[2^# - # - 1 &@ PrimeNu[#] &, 120] %Y A376504 Cf. A000005, A000295, A000961, A001221, A002110, A007947, A034444, A120944, A162306, A327517, A361373 (number of prime powers in row n of A162306), A374514 (number of divisors of n that are neither squarefree nor prime powers). %K A376504 nonn,easy %O A376504 1,30 %A A376504 _Michael De Vlieger_, Sep 25 2024