A378527 - OEIS

%I #8 Dec 01 2024 13:40:44

%S 1,-2,-3,0,-5,6,-7,0,-1,10,-11,-1,-13,14,14,-1,-17,2,-19,-1,20,22,-23,

%T 2,-1,26,3,-1,-29,-28,-31,2,32,34,34,3,-37,38,38,2,-41,-40,-43,-1,8,

%U 46,-47,3,-1,2,50,-1,-53,-6,54,2,56,58,-59,8,-61,62,10,0,64,-64,-67,-1,68,-68,-71,-6,-73,74,8,-1,76,-76,-79,5

%N Dirichlet inverse of A378546.

%H Antti Karttunen, <a href="/A378527/b378527.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} A378546(n/d) * a(d).

%F a(n) = Sum_{d|n} A055615(d)*A369974(n/d).

%F a(n) = Sum_{d|n} A023900(d)*A378528(n/d).

%o (PARI)

%o A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };

%o A369001(n) = !(A083345(n)%2);

%o A378546(n) = sumdiv(n,d,d*A369001(n/d));

%o memoA378527 = Map();

%o A378527(n) = if(1==n,1,my(v); if(mapisdefined(memoA378527,n,&v), v, v = -sumdiv(n,d,if(d<n,A378546(n/d)*A378527(d),0)); mapput(memoA378527,n,v); (v)));

%Y Cf. A023900, A055615, A369974, A378546.

%Y Cf. also A378525, A378526, A378528.

%K sign

%O 1,2

%A _Antti Karttunen_, Dec 01 2024