A377985 a(n) = 2*n - phi(A003961(n)), where phi is Euler totient function and A003961 is fully multiplicative function with a(prime(i)) = prime(i+1).

1, 2, 2, 2, 4, 4, 4, -2, -2, 8, 10, 0, 10, 8, 6, -22, 16, -4, 16, 4, 2, 20, 18, -24, 8, 20, -46, -4, 28, 12, 26, -98, 18, 32, 10, -48, 34, 32, 14, -28, 40, 4, 40, 16, -30, 36, 42, -120, -12, 16, 30, 8, 48, -92, 38, -68, 26, 56, 58, -24, 56, 52, -74, -358, 34, 36, 64, 28, 26, 20, 70, -216, 68, 68, -18, 20, 34, 28

Offset: 1

Author

Antti Karttunen, Nov 16 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000010, A003961, A003972, A008683.

Möbius transform of A377984.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A377985(n) = (2*n - eulerphi(A003961(n)));

Formula

a(n) = 2*n - A003972(n).

a(n) = Sum_{d|n} A008683(n/d) * A377984(d).