A070272 Numbers n such that reverse(n) = phi(n) + sigma(n).

275, 295, 2995, 299995, 2999995, 278736495, 299999995, 299999999995

Offset

1,1

Comments

For n>0 5*(6*10^A056716(n)-1) is in this sequence. In fact if p = 6*10^n-1 is prime and n>0 (p>5) then m = 5*p is in the sequence. That's because phi(m) = phi(5*p) = 4*(6*10^n-2) = 24*10^n-8 and sigma(m)= 6*6*10^n, so phi(m) + sigma(m) = 6*10^(n+1)-8 = 5.(9)(n).2 = reversal(2.(9)(n).5) = reversal (3*10^(n+1)-5) = reversal(m)(dot between numbers means concatenation and "(9)(n)" means number of 9's is n). For example 299999995 is in the sequence because 6*10^7-1 is prime and 299999995 = 5*(6*10^7-1); 299999999995 is in sequence because 6*10^10-1 is prime and 299999999995 = 5*(6*10^10-1). Next term is greater than 80000000. - Farideh Firoozbakht, Jan 11 2005

Next term is greater than 10^9. - Farideh Firoozbakht, Jan 23 2005

a(9) > 10^13. - Giovanni Resta, Feb 08 2014

Links

Table of n, a(n) for n=1..8.

Example

Reverse(275) = 572 = 200 + 372 = phi(275) + sigma(275).

Mathematica

Select[Range[10^6], FromDigits[Reverse[IntegerDigits[ # ]]] == EulerPhi[ # ] + DivisorSigma[1, # ] &]

Crossrefs

Cf. A056716, A102284.

Sequence in context: A214111 A344731 A023681 * A066127 A062377 A157489

Adjacent sequences: A070269 A070270 A070271 * A070273 A070274 A070275

Keyword

base,nonn

Author

Joseph L. Pe, May 12 2002

Extensions

One more term from Farideh Firoozbakht, Jan 11 2005

More terms from Farideh Firoozbakht, Jan 23 2005

a(8) from Giovanni Resta, Nov 03 2012

Status

approved