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A070820
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Difference between n-th prime and the value of Commutator[Phi,P]=Commutator[A000010, A006530] at the same prime argument.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| a(n)=A000040(n)-A070812[A000040(n)]=p[n]-A070819(n); Odd differences(=3) appear only at Fermat-primes, i.e. at prime indices of n={2, 3, 7, 55, 6543}. a(1)=2-0 by convention.
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EXAMPLE
| n=100: p[100]=541,Phi[541]=540,P[540]=5, P[541]=541,Phi[541]=540, A070819(100)=535, a(100)=A070820(100)=541-535.
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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}]
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CROSSREFS
| Cf. A000010, A006530, A000040, A070812, A070813, A070819.
Sequence in context: A157725 A081536 A023154 * A031501 A203996 A059442
Adjacent sequences: A070817 A070818 A070819 * A070821 A070822 A070823
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), May 10 2002
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