A112721 - OEIS

%I #31 Jul 21 2025 21:41:15

%S 1,44,84,5676,32186,35097,128476,527048,700298,12141094,43874279,

%T 58730238,303387848,2277279428

%N Numbers m such that phi(m) = d_1^1 + d_2^2 + ... + d_k^k where d_1 d_2 ... d_k is the decimal expansion of m.

%C a(15) > 6*10^10. - _Donovan Johnson_, Nov 09 2010

%C All terms of this sequence are less than 2 * 10^42. - _Charles R Greathouse IV_, May 11 2012

%C a(15) > 10^12. - _Giovanni Resta_, Apr 12 2017

%e phi(12141094) = 1^1 + 2^2 + 1^3 + 4^4 + 1^5 + 0^6 + 9^7 + 4^8 = 4848768 so 12141094 is in the sequence.

%t Do[d=IntegerDigits[n];k=Length[d];If[EulerPhi[n]==Sum[d[[j]]^j, {j, k}], Print[n]], {n, 30000000}]

%Y Cf. A000010, A032799, A035138, A112718, A112719, A112720.

%K base,fini,more,nonn

%O 1,2

%A _Farideh Firoozbakht_, Sep 17 2005

%E a(11)-a(12) from _Farideh Firoozbakht_, Jan 04 2009

%E a(13)-a(14) from _Donovan Johnson_, Nov 09 2010