A071525 -id:A071525 - cp's OEIS frontend

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

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

Offset: 1

Farideh Firoozbakht, Dec 26 2007

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

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

Cf. A071525, A000010, A000203.

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

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

a(7) from Donovan Johnson, Oct 24 2013

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

A135240 Numbers n such that phi(sigma(n))=2n.

Original entry on oeis.org

36, 20575296

Offset: 1

Farideh Firoozbakht, Dec 26 2007

No other terms below 10^10. - Max Alekseyev, Sep 25 2009

6.5*10^12 < a(3) <= 180577942272000000. We also have phi(sigma(n)) = 3*n for n = 144982963520227123200 and phi(sigma(n)) = 4*n for n = 16310583396025551360000 thus these may not be the smallest such n. - Giovanni Resta, Sep 13 2018

			phi(sigma(20575296))=phi(71238999)=41150592=2*20575296, so 20575296 is in the sequence.

Cf. A071525, A135238, A135239.

Do[If[EulerPhi[DivisorSigma[1,n]]==2n,Print[n]],{n,350000000}]

cp's OEIS Frontend

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

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