A378229 - OEIS

%I #8 Nov 24 2024 09:29:32

%S 1,-9,-20,18,-42,180,-88,0,75,378,-156,-360,-238,792,840,0,-342,-675,

%T -460,-756,1760,1404,-696,0,245,2142,0,-1584,-930,-7560,-1184,0,3120,

%U 3078,3696,1350,-1558,4140,4760,0,-1806,-15840,-2068,-2808,-3150,6264,-2544,0,847,-2205,6840,-4284,-3186,0,6552,0,9200,8370

%N Dirichlet inverse of A341529, where A341529(n) = sigma(n) * A003961(n), and A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

%C Multiplicative because A341529 is.

%H Antti Karttunen, <a href="/A378229/b378229.txt">Table of n, a(n) for n = 1..20000</a>

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

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

%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A341529(n/d) * a(d).

%o (PARI)

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

%o A341529(n) = (sigma(n)*A003961(n));

%o memoA378229 = Map();

%o A378229(n) = if(1==n,1,my(v); if(mapisdefined(memoA378229,n,&v), v, v = -sumdiv(n,d,if(d<n,A341529(n/d)*A378229(d),0)); mapput(memoA378229,n,v); (v)));

%Y Dirichlet inverse of A341529.

%Y Cf. also A378228.

%K sign,mult

%O 1,2

%A _Antti Karttunen_, Nov 23 2024