A070820 Difference between n-th prime and the value of commutator[phi,gpf] = commutator[A000010, A006530] at the same prime argument.
2, 3, 3, 4, 6, 4, 3, 4, 12, 8, 6, 4, 6, 8, 24, 14, 30, 6, 12, 8, 4, 14, 42, 12, 4, 6, 18, 54, 4, 8, 8, 14, 18, 24, 38, 6, 14, 4, 84, 44, 90, 6, 20, 4, 8, 12, 8, 38, 114, 20, 30, 18, 6, 6, 3, 132, 68, 6, 24, 8, 48, 74, 18, 32, 14, 80, 12, 8, 174, 30, 12, 180, 62, 32, 8, 192, 98, 12, 6, 18
Offset: 1
Keywords
Examples
For n=100: prime(100) = 541, phi(541) = 540, gpf(540) = 5, gpf(541) = 541, phi(541) = 540, A070819(100) = 535, a(100) = A070820(100) = 541 - 535.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] f[x_] := EulerPhi[pf[x]]-pf[EulerPhi[x]] Table[Prime[w]-f[Prime[w]], {w, 2, 128}] -
PARI
a(n)=if(n>1, my(f=factor(prime(n)-1)[, 1]); f[#f]+1, 2)