A101697 - OEIS

%I #7 Mar 19 2025 10:26:12

%S 1,67585,84466,854696

%N Numbers n such that phi(n) is equal to d_1!+d_2!+...+d_k!, where d_1 d_2 ... d_k is the decimal expansion of n.

%H Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_16">Fascinating Factorials</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 16, 411-442.

%e 854696 is in the sequence because phi(854696)=8!+5!+4!+6!+9!+6!.

%t Do[h = IntegerDigits[n]; l = Length[h]; If[EulerPhi[n] == Sum[h[[k]]!, {k, l}], Print[n]], {n, 10000000}]

%Y Cf. A100416.

%K base,fini,full,nonn

%O 1,2

%A _Farideh Firoozbakht_, Dec 12 2004