A378523 - OEIS

%I #7 Nov 30 2024 23:46:44

%S 1,-3,-4,2,-6,14,-8,0,3,20,-12,-14,-14,26,27,0,-18,-17,-20,-18,35,38,

%T -24,4,5,44,0,-22,-30,-109,-32,0,51,56,53,34,-38,62,59,4,-42,-137,-44,

%U -30,-30,74,-48,0,7,-27,75,-34,-54,6,77,4,83,92,-60,146,-62,98,-36,0,89,-193,-68,-42,99,-199,-72,-28,-74,116

%N Dirichlet inverse of A332993, where A332993 is defined as a(1) = 1, and for n > 1, a(n) = n + a(A032742(n)), and A032742 is the largest proper divisor.

%H Antti Karttunen, <a href="/A378523/b378523.txt">Table of n, a(n) for n = 1..20000</a>

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A332993(n/d) * a(d).

%o (PARI)

%o A332993(n) = if(1==n,n,n + A332993(n/vecmin(factor(n)[,1])));

%o memoA378523 = Map();

%o A378523(n) = if(1==n,1,my(v); if(mapisdefined(memoA378523,n,&v), v, v = -sumdiv(n,d,if(d<n,A332993(n/d)*A378523(d),0)); mapput(memoA378523,n,v); (v)));

%Y Cf. A032742, A332993.

%Y Cf. also A378524.

%K sign

%O 1,2

%A _Antti Karttunen_, Nov 30 2024