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A070813
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Even numbers 2m such that f[x]=Phi[P[x]]-P[Phi[x]] = 2m for some x, where P[m]=largest prime divisor of m, Phi[m]=totient[m].
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9
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OFFSET
| 1,2
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COMMENTS
| Solutions to A070812[x]=0 are in A007283, for A070812[x]=2 are in A070004.
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FORMULA
| a(n)=Fermat-primes minus 3 = A000215(n)-3
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EXAMPLE
| x=3,5,17,257,65537, P[x]=x, P[Phi[x]]=2, Phi[P[x]]=x-1, f[x]=x-1-2=x-3; so if x is a Fermat-prime, then value of commutator equals x-3, i.e. it is an even number.
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MATHEMATICA
| pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[ !Odd[s]&&Greater[s, 2], Print[{n, s}], {n, 3, 10000000}] Only 2, 254 and 65534 appear in printout of s. The sequence is provided by Union[{s}, {0, 2}].
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CROSSREFS
| Cf. A000010, A006530, A070812, A000215.
Sequence in context: A053846 A053855 A152476 * A156214 A187654 A015197
Adjacent sequences: A070810 A070811 A070812 * A070814 A070815 A070816
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KEYWORD
| nice,nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), May 09 2002
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