A378754 -id:A378754 - cp's OEIS frontend

A378755 Dirichlet convolution of A033879 and A346248.

1, 0, 1, 2, 1, 2, 3, 10, 11, 2, 1, 14, 3, 6, 7, 42, 1, 26, 3, 14, 17, 2, 5, 70, 15, 6, 81, 34, 1, 22, 5, 170, 7, 2, 17, 146, 3, 6, 17, 70, 1, 54, 3, 14, 69, 10, 5, 326, 55, 34, 7, 34, 5, 234, 7, 162, 17, 2, 1, 138, 5, 10, 155, 682, 17, 22, 3, 14, 27, 54, 1, 730, 5, 6, 89, 34, 17, 54, 3, 326, 571, 2, 5, 318, 7, 6, 7

Offset: 1

Antti Karttunen, Dec 11 2024

nonn

Cf. A033879, A346248, A378754 (Dirichlet inverse).

A033879(n) = (n+n-sigma(n));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A252748(n) = (A003961(n) - (2*n));
memoA346248 = Map();
A346248(n) = if(1==n,1,my(v); if(mapisdefined(memoA346248,n,&v), v, v = -sumdiv(n,d,if(dA252748(n/d)*A346248(d),0)); mapput(memoA346248,n,v); (v)));
A378755(n) = sumdiv(n,d,A033879(d)*A346248(n/d));

a(n) = Sum_{d|n} A033879(d)*A346248(n/d).

A379106 Dirichlet convolution of A000120 and A323910, where A323910 is the Dirichlet inverse of the deficiency of n, and A000120 is the binary weight of n.

Original entry on oeis.org

1, 0, 0, 0, -2, 2, -3, 0, -3, 2, -7, 4, -9, 2, 2, 0, -14, 4, -15, 4, -1, 2, -18, 8, -8, 2, -4, 4, -24, 2, -25, 0, -2, 2, 5, 12, -33, 2, 0, 8, -37, 0, -38, 4, 10, 2, -41, 16, -20, 0, 2, 4, -48, 2, 15, 8, 0, 2, -53, 12, -55, 2, 19, 0, 16, -8, -63, 4, -3, -4, -66, 32, -69, 2, -2, 4, 18, -12, -73, 16, -15, 2, -78, 8, 30

Offset: 1

Antti Karttunen, Dec 16 2024

sign

Cf. A000120, A033879, A323910, A379107 (Dirichlet inverse).

Cf. also A294898, A378754, A378756.

A033879(n) = (n+n-sigma(n));
memoA323910 = Map();
A323910(n) = if(1==n,1,my(v); if(mapisdefined(memoA323910,n,&v), v, v = -sumdiv(n,d,if(dA033879(n/d)*A323910(d),0)); mapput(memoA323910,n,v); (v)));
A379106(n) = sumdiv(n,d,hammingweight(d)*A323910(n/d));

a(n) = Sum_{d|n} A000120(d)*A323910(n/d).

cp's OEIS Frontend

A378755 Dirichlet convolution of A033879 and A346248.

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