A346246 Dirichlet inverse of A344587, 2*A003961(n) - sigma(A003961(n)).

1, -2, -4, -1, -6, 10, -10, -2, -3, 14, -12, 4, -16, 22, 26, -4, -18, 2, -22, 6, 42, 26, -28, 6, -5, 34, -6, 10, -30, -66, -36, -8, 50, 38, 62, 7, -40, 46, 66, 10, -42, -106, -46, 12, 14, 58, -52, 8, -9, 2, 74, 16, -58, -2, 74, 18, 90, 62, -60, -18, -66, 74, 26, -16, 98, -126, -70, 18, 114, -150, -72, 18, -78, 82, 12, 22

Offset: 1

Author

Antti Karttunen, Jul 19 2021

Keywords

• sign
• look

Comments

Dirichlet inverse of the deficiency of prime shifted n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32768
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A003973, A323910, A344587, A346247, A346251 (positions of zeros).

Cf. also A346235, A346248, A346254.

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];

Formula

a(n) = A323910(A003961(n)).

a(n) = A346247(n) - A344587(n).