A103113 Numbers n such that phi(n)=phi(d_1^d_1)*phi(d_2^d_2)*...*phi(d_k^d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

1, 113125, 2322432, 21332611, 2115124224, 3111423252, 3412115322, 12451223232, 116222114125, 1141433232511, 2231521231226, 2334121141253, 3222154622111, 4211413132352, 15123362231122, 21123234615111, 32125124213611, 114231133412352, 233152112133612

Offset

1,2

Comments

a(38) (if it exists) >= 10^18. - Hiroaki Yamanouchi, Sep 10 2014

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..37

Example

21332611 is in the sequence because phi(21332611)=phi(2^2)*phi(1^1)*phi(3^3)*phi(3^3)*phi(2^2)*phi(6^6)*phi(1^1)*phi(1^1).

Mathematica

Do[h=IntegerDigits[m]; l=Length[h]; If[Min[h]>0&&EulerPhi[m]== Product[EulerPhi[h[[k]]^h[[k]]], {k, l}], Print[m]], {m, 200000000}]

Crossrefs

Cf. A104898.

Sequence in context: A177275 A303999 A252036 * A179922 A122511 A172549

Adjacent sequences: A103110 A103111 A103112 * A103114 A103115 A103116

Keyword

nonn,base

Author

Farideh Firoozbakht, Mar 29 2005

Extensions

a(5)-a(17) from Max Alekseyev, May 10 2009, May 05 2010, Aug 22 2013

a(18)-a(19) from Hiroaki Yamanouchi, Sep 10 2014

Status

approved