A373976 - OEIS

%I #7 Jun 24 2024 17:10:07

%S 0,0,0,0,0,1,0,1,0,1,0,2,0,0,-1,1,0,0,0,1,0,1,0,2,0,0,1,2,0,1,0,3,0,1,

%T -1,2,0,0,-2,3,0,0,0,1,2,0,0,4,0,0,-1,2,0,3,-2,3,0,1,0,1,0,0,2,3,-1,

%U -1,0,1,0,1,0,2,0,0,2,2,-1,0,0,4,1,1,0,2,0,-1,-3,3,0,3,-1,0,0,0,-2,5,0,-1,2,2,0

%N a(n) = A001222(n) - A001222(A001414(n)), where A001222 is bigomega, the number of prime factors with multiplicity, and A001414 is sopfr, sum of prime factors with multiplicity. a(1) = 0 by convention.

%H Antti Karttunen, <a href="/A373976/b373976.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A001222(n) - A342956(n).

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.

%o A373976(n) = if(1==n, 0, bigomega(n)-bigomega(A001414(n)));

%Y Cf. A001222, A001414, A342956.

%Y Cf. also A045835.

%K sign

%O 1,12

%A _Antti Karttunen_, Jun 24 2024