A063690 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.

1, 12, 20, 44, 68, 74, 146, 284, 2204, 6884, 61454, 82934, 407924, 2792144, 3988424, 8380448, 37762394, 191916944, 206846955, 705182864, 867648044, 874419272, 874628864

Offset

1,2

Comments

No more terms through 10^7. - Ryan Propper, Aug 26 2005

No more terms below 10^9. - Amiram Eldar, Jul 22 2019

Links

Table of n, a(n) for n=1..23.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A048783, A000040, A000010, A000005.

Sequence in context: A211415 A209973 A282754 * A229355 A259174 A109788

Adjacent sequences: A063687 A063688 A063689 * A063691 A063692 A063693

Keyword

nonn

Author

Jason Earls, Aug 23 2001

Extensions

More terms from David Wasserman, Jul 18 2002

3 more terms from Ryan Propper, Aug 26 2005

a(17)-a(23) from Amiram Eldar, Jul 22 2019

Status

approved