A230004 Numbers n such that phi(n) + sigma(n) = reversal(n) + 4.

499, 2836, 4999, 49999, 280036, 4999999, 28000036, 283682836, 2800000000036

Offset: 1

Author

Farideh Firoozbakht, Nov 07 2013

Keywords

• nonn
• base

Comments

If p=5*10^m-1 is prime (m is a term of A056712) then p is in the sequence.

Let p(m,n) = 10^(m+3)*(7*10^(m+2)+92)*(10^((m+4)*n)-1)/(10^(m+4)-1) +7*10^(m+1)+9, if m>0, n>=0 and p(m,n) is prime then 4*p(m,n) is in the sequence.

All known terms are of these two forms.

What is the smallest term of the sequence which is not of the form p or 4*p where p is prime?

Note that a(2)=4*p(1,0), a(5)=4*p(3,0), a(7)=4*p(5,0) and a(8)=4*p(1,1).

Examples

			phi(499)+sigma(499) = 498+500 = 994+4 = reversal(499)+4, so 499 is in the sequence.
		

Crossrefs

Cf. A000010, A000203, A004086, A056712, A230005.

Programs

Mathematica

r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[If[DivisorSigma[1,n] + EulerPhi[n] == r[n] + 4, Print[n]], {n,1050000000}]
Select[Range[5*10^6],EulerPhi[#]+DivisorSigma[1,#]==IntegerReverse[#]+4&] (* The program generates the first 6 terms of the sequence. *) (* Harvey P. Dale, Dec 28 2024 *)

PARI

is(n)=subst(Polrev(digits(n)),'x,10)+4==eulerphi(n)+sigma(n) \\ Charles R Greathouse IV, Nov 08 2013

Extensions

a(9) from Giovanni Resta, Feb 06 2014