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A063690
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Numbers n such that n-th prime - phi(n) - d(n) = (n+1)-th prime - phi(n+1) - d(n+1), where d(n) = number of divisors of n.
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0
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1, 12, 20, 44, 68, 74, 146, 284, 2204, 6884, 61454, 82934, 407924, 2792144, 3988424, 8380448, 37762394, 191916944, 206846955, 705182864, 867648044, 874419272, 874628864
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OFFSET
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1,2
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COMMENTS
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LINKS
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MATHEMATICA
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Do[If[Prime[n] - EulerPhi[n] - DivisorSigma[0, n] == Prime[n+1] - EulerPhi[n+1] - DivisorSigma[0, n+1], Print[n]], {n, 1, 10^7}] (* Ryan Propper, Aug 26 2005 *)
Transpose[SequencePosition[Table[Prime[n]-EulerPhi[n]-DivisorSigma[0, n], {n, 10^7}], {x_, x_}]][[1]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, Feb 12 2016 *)
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PROG
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(PARI) for(n=1, 40000, if(prime(n) - eulerphi(n) - numdiv(n)==prime(n+1) - eulerphi(n+1) - numdiv(n+1), print(n)))
(PARI) a1 = -1; n = 1; forprime(p=1, 10^6, a2 = p - eulerphi(n) - numdiv(n); if(a1 == a2, print1(n-1, ", ")); a1 = a2; n++) \\ Amiram Eldar, Jul 22 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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