A135238 Numbers n such that phi(sigma(n)) = reversal(n).

1, 2, 8, 2991, 65034, 880374, 2346534651, 46464826662, 234065340651

Offset

1,2

Comments

If both numbers 10^m-3 & 5*10^(m-1)-1 are primes and n=3*(10^m-3) then phi(sigma(n))=reversal(n), namely n is in the sequence (the proof is easy). Conjecture: n=2991 is the only such term of the sequence. there is no further term up to 35*10^7.

There are no other terms up to 10^10. - Donovan Johnson, Oct 24 2013

If p and 2*p-1 are primes, where p = 3900000*100^t + 108900*10^t + 109, then 6*p-3 is in the sequence. This happens at least for t=1 (2346534651), t=2 (234065340651), t=11, and t=76. - Giovanni Resta, Aug 09 2019

Links

Table of n, a(n) for n=1..9.

Example

phi(sigma(880374)) = phi(1920960) = 473088 = reversal(880374), so 880374 is in the sequence.

Mathematica

reversal[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; Do[If[EulerPhi[DivisorSigma[1, n]]==reversal[n], Print[n]], {n, 350000000}]

Prog

(PARI) isok(n) = eulerphi(sigma(n)) == fromdigits(Vecrev(digits(n))); \\ Michel Marcus, Aug 09 2019

Crossrefs

Cf. A071525, A000010, A000203.

Sequence in context: A054874 A174736 A324567 * A133376 A179056 A160814

Adjacent sequences: A135235 A135236 A135237 * A135239 A135240 A135241

Keyword

nonn,base,more

Author

Farideh Firoozbakht, Dec 26 2007

Extensions

a(7) from Donovan Johnson, Oct 24 2013

a(8)-a(9) from Giovanni Resta, Aug 09 2019

Status

approved