A378754 - OEIS

%I #7 Dec 11 2024 20:17:59

%S 1,0,-1,-2,-1,-2,-3,-10,-10,-2,-1,-10,-3,-6,-5,-38,-1,-22,-3,-10,-11,

%T -2,-5,-42,-14,-6,-60,-22,-1,-14,-5,-130,-5,-2,-11,-76,-3,-6,-11,-42,

%U -1,-30,-3,-10,-36,-10,-5,-158,-46,-30,-5,-22,-5,-144,-5,-78,-11,-2,-1,-58,-5,-10,-64,-422,-11,-14,-3,-10,-17,-30

%N Dirichlet convolution of -A252748 and A323910.

%H Antti Karttunen, <a href="/A378754/b378754.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F a(n) = Sum_{d|n} -A252748(d)*A323910(n/d).

%o (PARI)

%o A033879(n) = (n+n-sigma(n));

%o memoA323910 = Map();

%o A323910(n) = if(1==n,1,my(v); if(mapisdefined(memoA323910,n,&v), v, v = -sumdiv(n,d,if(d<n,A033879(n/d)*A323910(d),0)); mapput(memoA323910,n,v); (v)));

%o A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A252748(n) = (A003961(n) - (2*n));

%o A378754(n) = sumdiv(n,d,-A252748(d)*A323910(n/d));

%Y Cf. A033879, A252748, A323910, A378755 (Dirichlet inverse).

%K sign,new

%O 1,4

%A _Antti Karttunen_, Dec 11 2024