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