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Search: id:A070162
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| A070162 |
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n is such that n-Phi[n]-1 is prime number. |
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3
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| 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 26, 34, 36, 38, 40, 42, 44, 46, 48, 50, 56, 58, 60, 62, 64, 72, 74, 78, 80, 82, 84, 86, 88, 92, 94, 100, 106, 108, 116, 118, 122, 126, 134, 136, 142, 146, 150, 152, 156, 158, 162, 164, 166, 178, 180, 182, 192, 194, 198, 202, 204
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Maximal solution is either n=2p or in case of M Mersenne- primes: n=2(M+1) and f[n]=p or f[n]=M.
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FORMULA
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f[n]=n-A000010(n)-1=A051953(n)-1 is prime.
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EXAMPLE
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n=192: phi[192]=64, cototient[192]=128, n-phi[192]-1=127 is prime; n=2p: 2p-phi[2p]-1=2p-p+1-1=p, so 2*prime is always solution; n=2^(q+1): where q is a Mersenne-prime-exponent, then cototient[n]-1=2^(p+1)-2^p-1=2^p-1, which is the corresponding Mersenne- prime; if n={192,224,248,254,256} give p=127; if n={72,80,88,92,94} give p=47.
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MATHEMATICA
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Do[s=n-EulerPhi[n]-1; If[PrimeQ[s], Print[n, s]], n, 1, 10000]
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CROSSREFS
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Cf. A000010, A051953.
Sequence in context: A054047 A056653 A062973 this_sequence A030550 A024321 A102106
Adjacent sequences: A070159 A070160 A070161 this_sequence A070163 A070164 A070165
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 26 2002
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