A104906 Numbers k such that d(k)*reversal(k)=phi(k), where d(k) is number of positive divisors of k.

1, 10, 831, 8310

Offset

1,2

Comments

If k is a term of this sequence and gcd(10,k)=1 then 10*k is also in the sequence because reversal(10*n)=reversal(n); d(10)=phi(10) and both functions d & phi are multiplicative.

a(5) > 10^12. - Giovanni Resta, Apr 25 2017

No prime terms exist, that is, for terms k > 1, d(k) >= 3. Also, there are no terms of the forms p^3 or p^6 with a prime p. Also, terms can end with digit 0 or 1 only. - Max Alekseyev, Mar 29 2026

Links

Table of n, a(n) for n=1..4.

Example

8310 is in the sequence because d(8310)=16; reversal(8310)=138; phi(8310)=2208 & 16*138=2108.

Mathematica

reversal[n_]:= FromDigits[Reverse[IntegerDigits[n]]]; Do[If[DivisorSigma[0, n]*reversal[n] == EulerPhi[n], Print[n]], {n, 350000000}]

Prog

(PARI) isok(k) = numdiv(k)*fromdigits(Vecrev(digits(k))) == eulerphi(k); \\ Michel Marcus, Oct 31 2025

Crossrefs

Cf. A000005, A000010, A004086.

Cf. A063903, A104904, A104905, A104907.

Sequence in context: A054944 A272854 A015093 * A396354 A378324 A013386

Adjacent sequences: A104903 A104904 A104905 * A104907 A104908 A104909

Keyword

nonn,base,more

Author

Farideh Firoozbakht, Apr 14 2005

Status

approved