A346247 Sum of A344587 (the deficiency of prime shifted n) and its Dirichlet inverse.

2, 0, 0, 4, 0, 16, 0, 12, 16, 24, 0, 16, 0, 40, 48, 37, 0, 28, 0, 28, 80, 48, 0, 36, 36, 64, 88, 52, 0, -48, 0, 114, 96, 72, 120, 54, 0, 88, 128, 68, 0, -64, 0, 64, 116, 112, 0, 92, 100, 68, 144, 88, 0, 124, 144, 132, 176, 120, 0, -12, 0, 144, 204, 349, 192, -72, 0, 100, 224, -72, 0, 128, 0, 160, 160, 124, 240, -88, 0, 182

Offset: 1

Author

Antti Karttunen, Jul 19 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16383
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A323911, A344587, A346246.

Cf. also A346250.

Programs

PARI

up_to = 16384;
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); }; \\ From A003961
A344587(n) = { my(u=A003961(n)); (u+u - sigma(u)); };
v346246 = DirInverseCorrect(vector(up_to,n,A344587(n)));
A346246(n) = v346246[n];
A346247(n) = (A344587(n)+A346246(n));

Formula

a(n) = A344587(n) + A346246(n).

a(n) = A323911(A003961(n)).