A364953 - OEIS

%I #10 Aug 30 2023 13:03:57

%S 1,-1,-2,-1,-4,2,0,-1,-8,4,12,2,8,0,0,-1,-16,8,24,4,56,-12,-8,2,48,-8,

%T -40,0,-16,0,0,-1,-32,16,48,8,112,-24,-16,4,240,-56,-232,-12,-208,8,0,

%U 2,224,-48,-208,-8,-528,40,64,0,-288,16,112,0,32,0,0,-1,-64,32,96,16,224,-48,-32,8,480,-112,-464,-24

%N a(n) = A364952(A005940(1+n)), where A364952 is Dirichlet inverse of A364557, which is Möbius transform of A005941 [the inverse permutation of A005940].

%H Antti Karttunen, <a href="/A364953/b364953.txt">Table of n, a(n) for n = 0..16384</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

%o A364557(n) = if(1==n, 1, 2^(primepi(vecmax(factor(n)[, 1]))+(bigomega(n)-omega(n))-1));

%o memoA364952 = Map();

%o A364952(n) = if(1==n,1,my(v); if(mapisdefined(memoA364952,n,&v), v, v = -sumdiv(n,d,if(d<n,A364557(n/d)*A364952(d),0)); mapput(memoA364952,n,v); (v)));

%o A364953(n) = A364952(A005940(1+n));

%Y Cf. A005940, A005941, A364557, A364952.

%Y Cf. also A364567, A364575.

%K sign

%O 0,3

%A _Antti Karttunen_, Aug 29 2023