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 A081400 #13 May 25 2017 22:05:49 %S A081400 0,0,0,-1,0,1,0,-2,-1,1,0,1,0,1,1,-3,0,1,0,1,1,1,0,1,-1,1,-2,1,0,4,0, %T A081400 -4,1,1,1,1,0,1,1,1,0,4,0,1,1,1,0,1,-1,1,1,1,0,1,1,1,1,1,0,6,0,1,1,-5, %U A081400 1,4,0,1,1,4,0,1,0,1,1,1,1,4,0,1,-3,1,0,6,1,1,1,1,0,6,1,1,1,1,1,1,0,1,1,1,0,4,0,1,4,1,0,1,0,4,1,1,0,4,1,1,1,1,1,8,-1,1 %N A081400 a(n) = d(n) - bigomega(n) - A005361(n). %H A081400 Antti Karttunen, <a href="/A081400/b081400.txt">Table of n, a(n) for n = 1..10000</a> %F A081400 a(n) = A000005(n) - A001222(n) - A005361(n). %e A081400 Negative for true prime powers; zero for 1 and primes; see also A030231, A007304, A034683, A075819 etc. to judge about positivity or magnitude. %o A081400 (PARI) a(n) = my(f=factor(n)); numdiv(n) - bigomega(n) - prod(k=1, #f~, f[k,2]); \\ _Michel Marcus_, May 25 2017 %o A081400 (Python) %o A081400 from sympy import primefactors, factorint, divisor_count %o A081400 from operator import mul %o A081400 def bigomega(n): return 0 if n==1 else bigomega(n/primefactors(n)[0]) + 1 %o A081400 def a005361(n): %o A081400 f=factorint(n) %o A081400 return 1 if n==1 else reduce(mul, [f[i] for i in f]) %o A081400 def a(n): return divisor_count(n) - bigomega(n) - a005361(n) # _Indranil Ghosh_, May 25 2017 %Y A081400 Cf. A000005, A001222, A005361, A030231, A030230, A007304, A034683, A075819. %K A081400 sign %O A081400 1,8 %A A081400 _Labos Elemer_, Mar 28 2003