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%I #3 Apr 03 2023 10:36:11
%S 1,2,672,34992,139968
%N Numbers n such that n=(d_1*d_2*...*d_k)*phi(d_1+d_2+...+d_k) where d_1 d_2... d_k is the decimal expansion of n.
%C Conjecture: 139968 is the largest term. Except for the first term, all terms are even. 139968 is also in A120121 & A120122, so it has a very pleasant property (see the Comments lines of A120121).
%H Prime Curios, <a href="https://t5k.org/curios/page.php/139968.html">139968</a>.
%e 34992 is in the sequence because 34992=(3*4*9*9*2)*phi(3+4+9+9+2).
%t Do[If[h = IntegerDigits[n]; l = Length[h]; n == Product[h[[k]], {k, l}]*EulerPhi[Sum[h[[k]], {k, l}]], Print[n]], {n, 50000000}]
%Y Cf. A120121, A120122.
%K base,nonn
%O 1,2
%A _Farideh Firoozbakht_, Aug 12 2006
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