A347100 a(n) = phi(A003961(n)) - phi(n), where A003961 is the prime shift towards larger primes, and phi is Euler totient function.
0, 1, 2, 4, 2, 6, 4, 14, 14, 8, 2, 20, 4, 14, 16, 46, 2, 34, 4, 28, 28, 14, 6, 64, 22, 20, 82, 48, 2, 40, 6, 146, 28, 20, 36, 108, 4, 26, 40, 92, 2, 68, 4, 52, 96, 34, 6, 200, 68, 64, 40, 72, 6, 182, 32, 156, 52, 32, 2, 128, 6, 42, 164, 454, 48, 76, 4, 76, 68, 96, 2, 336, 6, 44, 128, 96, 60, 104, 4, 292, 446, 44, 6
Offset: 1
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Mathematica
f[p_, e_] := NextPrime[p]^e; a[n_] := EulerPhi[Times @@ f @@@ FactorInteger[n]] - EulerPhi[n]; Array[a, 100] (* Amiram Eldar, Nov 27 2021 *)
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PARI
A347100(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (eulerphi(factorback(f))-eulerphi(n)); };
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PARI
A336853(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)-n); }; A347100(n) = sumdiv(n,d,moebius(n/d)*A336853(d));
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