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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. 0
1, 12, 20, 44, 68, 74, 146, 284, 2204, 6884, 61454, 82934, 407924, 2792144, 3988424, 8380448, 37762394, 191916944, 206846955, 705182864, 867648044, 874419272, 874628864 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 12:51 EST 2020. Contains 338947 sequences. (Running on oeis4.)