A353420 -id:A353420 - cp's OEIS frontend

A353336 Sum of A353420 and its Dirichlet inverse.

2, 0, 0, 1, 0, 4, 0, 1, 4, 6, 0, 2, 0, 8, 12, 1, 0, 14, 0, 3, 16, 10, 0, 2, 9, 12, 28, 4, 0, 12, 0, 1, 20, 14, 24, 9, 0, 16, 24, 3, 0, 22, 0, 5, 66, 20, 0, 2, 16, 25, 28, 6, 0, 56, 30, 4, 32, 22, 0, 12, 0, 26, 100, 1, 36, 24, 0, 7, 40, 28, 0, 9, 0, 28, 86, 8, 40, 34, 0, 3, 157, 30, 0, 19, 42, 32, 44, 5, 0, 52, 48

Offset: 1

Antti Karttunen, Apr 20 2022

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The first negative term is a(255255) = -11936.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from indices in prime factorization

Cf. A003961, A126760, A353420 (also a quadrisection of this sequence), A353335.

Cf. also A323882, A323894, A349135.

up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A126760(n) = {n&&n\=3^valuation(n, 3)<A126760
A353420(n) = A126760(A003961(n));
v353335 = DirInverseCorrect(vector(up_to,n,A353420(n)));
A353335(n) = v353335[n];
A353336(n) = (A353420(n)+A353335(n));

a(n) = A353420(n) + A353335(n).

For n > 1, a(n) = -Sum_{d|n, 1A353420(d) * A353335(n/d).

A353335 Dirichlet inverse of A353420.

Original entry on oeis.org

1, -1, -2, 0, -3, 2, -4, 0, -5, 3, -5, 0, -6, 4, 0, 0, -7, 5, -8, 0, -3, 5, -10, 0, -8, 6, -14, 0, -11, 0, -13, 0, -2, 7, -2, 0, -14, 8, -5, 0, -15, 3, -16, 0, 7, 10, -18, 0, -25, 8, -4, 0, -20, 14, -1, 0, -7, 11, -21, 0, -23, 13, 8, 0, -4, 2, -24, 0, -9, 2, -25, 0, -27, 14, 4, 0, -8, 5, -28, 0, -52, 15, -30, 0, -3

Offset: 1

Antti Karttunen, Apr 20 2022

sign

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from indices in prime factorization

Cf. A003961, A126760, A353420, A353336.

up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A126760(n) = {n&&n\=3^valuation(n, 3)<A126760
A353420(n) = A126760(A003961(n));
v353335 = DirInverseCorrect(vector(up_to,n,A353420(n)));
A353335(n) = v353335[n];

a(1) = 1; a(n) = -Sum_{d|n, d < n} A353420(n/d) * a(d).

a(n) = A353336(n) - A353420(n).

cp's OEIS Frontend

A353336 Sum of A353420 and its Dirichlet inverse.

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