A376404 Dirichlet inverse of 2*phi(n) - phi(A003961(n)), where phi is Euler totient function and A003961(n) is fully multiplicative function with a(prime(i)) = prime(i+1).
1, 0, 0, 2, -2, 4, -2, 10, 8, 4, -8, 16, -8, 8, 8, 42, -14, 28, -14, 12, 16, 4, -16, 72, 6, 8, 64, 28, -26, 16, -24, 170, 8, 4, 20, 144, -32, 8, 16, 52, -38, 40, -38, 0, 40, 12, -40, 328, 30, 28, 8, 16, -46, 228, 24, 124, 16, 4, -56, 112, -54, 12, 96, 682, 32, -8, -62, -12, 24, 24, -68, 712, -66, 8, 56, 4, 32, 16
Offset: 1
Keywords
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Crossrefs
Programs
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PARI
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; A349754(n) = (eulerphi(A003961(n))-2*eulerphi(n)); memoA376404 = Map(); A376404(n) = if(1==n,1,my(v); if(mapisdefined(memoA376404,n,&v), v, v = -sumdiv(n,d,if(d
Formula
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA349754(n/d) * a(d).
a(n) = Sum_{d|n} A346248(d).