A349352 -id:A349352 - cp's OEIS frontend

A349378 a(n) = A349376(n) + A349377(n).

2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, 0, 0, 10, 9, 0, 0, -8, 0, -30, 0, -4, 0, 0, 24, 27, 0, 0, 0, 34, 0, -40, 0, -14, -6, 0, 0, -34, 16, -66, 0, -14, 0, 10, 42, 44, 0, 0, 0, 166, 0, 0, -8, 11, 42, -70, 0, -20, 0, -172, 0, -70, 0, 0, -42, -22, 56, -70, 0, -103, 1, 0, 0, 216, 60, 0, 0, 78

Offset: 1

Antti Karttunen, Nov 17 2021

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Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A006368, A006369, A349376, A349377.

Cf. also A349352, A349369.

A349378(n) = (A349376(n)+A349377(n)); \\ Needs also code from A349376 and A349377.

a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1A349376(d) * A349377(n/d). [As the sequences are Dirichlet inverses of each other]

A349351 Dirichlet inverse of A006368, "the amusical permutation", a(2n)=3n, a(4n+1)=3n+1, a(4n-1)=3n-1.

Original entry on oeis.org

1, -3, -2, 3, -4, 3, -5, -3, -3, 9, -8, 6, -10, 9, 5, 3, -13, 15, -14, 0, 4, 15, -17, -15, -3, 21, 0, 9, -22, 9, -23, -3, 7, 27, 14, -24, -28, 27, 11, -9, -31, 27, -32, 12, 18, 33, -35, 24, -12, 15, 14, 6, -40, 9, 23, -27, 13, 45, -44, -63, -46, 45, 27, 3, 31, 39, -50, 9, 16, 9, -53, 6, -55, 57, 12, 18, 22, 33, -59

Offset: 1

Antti Karttunen, Nov 15 2021

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Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A006368, A349352, A349368, A349377.

up_to = 20000;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA006368(n) = ((3*n)+(n%2))\(2+((n%2)*2));
v349351 = DirInverseCorrect(vector(up_to,n,A006368(n)));
A349351(n) = v349351[n];

a(1) = 1; a(n) = -Sum_{d|n, d < n} A006368(n/d) * a(d).

a(n) = A349352(n) - A006368(n).

A349369 Sum of A006369 and its Dirichlet inverse, where A006369 is the inverse of "amusical permutation", A006368.

Original entry on oeis.org

2, 0, 0, 9, 0, 12, 0, 3, 4, 42, 0, -10, 0, 54, 28, 37, 0, 16, 0, -41, 36, 90, 0, 60, 49, 102, 16, -39, 0, -84, 0, 11, 60, 138, 126, 30, 0, 150, 68, 221, 0, -92, 0, -81, 40, 186, 0, -72, 81, -61, 92, -79, 0, 36, 210, 259, 100, 234, 0, 394, 0, 246, 56, 149, 238, -172, 0, -121, 124, -352, 0, 8, 0, 294, -22, -119, 270

Offset: 1

Antti Karttunen, Nov 17 2021

sign

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A006369, A349368.

Cf. also A349352, A349378.

A006369(n) = if(!(n%3),(2/3)*n,(1/3)*if(1==(n%3),((4*n)-1),((4*n)+1)));
memoA349368 = Map();
A349368(n) = if(1==n,1,my(v); if(mapisdefined(memoA349368,n,&v), v, v = -sumdiv(n,d,if(dA006369(n/d)*A349368(d),0)); mapput(memoA349368,n,v); (v)));
A349369(n) = (A006369(n)+A349368(n));

a(n) = A006369(n) + A349368(n).

a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1A006369(d) * A349368(n/d).

cp's OEIS Frontend

A349378 a(n) = A349376(n) + A349377(n).

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A349351 Dirichlet inverse of A006368, "the amusical permutation", a(2n)=3n, a(4n+1)=3n+1, a(4n-1)=3n-1.

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PARI

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A349369 Sum of A006369 and its Dirichlet inverse, where A006369 is the inverse of "amusical permutation", A006368.

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Author

Keywords

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Programs

PARI

Formula