A353469 Sum of A353467 and its Dirichlet inverse.

2, 0, 0, 1, 0, -2, 0, -3, 1, 2, 0, 7, 0, -2, -2, 9, 0, -1, 0, -7, 2, 2, 0, -25, 1, -2, -3, 7, 0, 4, 0, -28, -2, 2, -2, 10, 0, -2, 2, 25, 0, -4, 0, -7, 7, 2, 0, 91, 1, -7, -2, 7, 0, 1, 2, -25, 2, -2, 0, -27, 0, 2, -7, 90, -2, 4, 0, -7, -2, 12, 0, -60, 0, -2, -1, 7, -2, -4, 0, -91, 9, 2, 0, 27, 2, -2, 2, 25, 0, -3, 2

Offset: 1

Author

Antti Karttunen, Apr 21 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A252463, A348717, A353467, A353468.

Cf. also A353459.

Programs

PARI

A252463(n) = if(!(n%2),n/2,my(f=factor(n)); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f));
memoA353467 = Map();
A353467(n) = if(1==n,1,my(v); if(mapisdefined(memoA353467,n,&v), v, v = -sumdiv(n,d,if(dA353467(A252463(n/d))*A353467(d),0)); mapput(memoA353467,n,v); (v)));
A353469(n) = (A353467(n)+A353467(A252463(n)));

Formula

a(n) = A353467(n) + A353468(n) = A353467(n) + A353467(A252463(n)).

For n > 1, a(n) = -Sum_{d|n, 1A353467(d) * A353468(n/d). [As the sequences are Dirichlet inverses of each other]

For all n >= 1, a(n) = a(A003961(n)) = a(A348717(n)).