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A070819
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Values of Commutator[Phi,P]=Commutator[A000010, A006530] at prime arguments; a(1)=0 by convention.
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1
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0, 0, 2, 3, 5, 9, 14, 15, 11, 21, 25, 33, 35, 35, 23, 39, 29, 55, 55, 63, 69, 65, 41, 77, 93, 95, 85, 53, 105, 105, 119, 117, 119, 115, 111, 145, 143, 159, 83, 129, 89, 175, 171, 189, 189, 187, 203, 185, 113, 209, 203, 221, 235, 245, 254, 131, 201, 265, 253, 273
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| a(n)=Phi[P[p(n)]-P[Phi[p(n)]]=A070812[A000040(n)] where Phi(w)=Euler-totient of w, P(w) is the largest prime factor of w and p[w]=w-th prime number. So a(n)=[p(n)-1]-q=p(n)-1-q. See also A070813 when q=2.
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EXAMPLE
| n=100, p[100]=541, Phi[541]=540, P[540]=5, P[541]=541,Phi[541]=540, a(100)=540-5=535.
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MATHEMATICA
| pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] f[x_] := EulerPhi[pf[x]]-pf[EulerPhi[x]] Table[f[Prime[w]], {w, 1, 128}]
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CROSSREFS
| Cf. A000010, A006530, A000040, A070812, A070813.
Sequence in context: A175125 A171925 A057225 * A195667 A005244 A058541
Adjacent sequences: A070816 A070817 A070818 * A070820 A070821 A070822
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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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