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%I #3 Apr 03 2023 10:36:11
%S 1,2,24,139968
%N Numbers n such that n=phi(d_1*d_2*...*d_k)*(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 the sequences A120121 & A120123, 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 24 is in the sequence because 24=phi(2*4)*(2+4).
%t Do[If[h = IntegerDigits[n]; l = Length[h]; n == EulerPhi[ Product[h[[k]], {k, l}]]*Sum[h[[k]], {k, l}], Print[n]], {n, 100000000}]
%Y Cf. A120121, A120123.
%K base,fini,nonn
%O 1,2
%A _Farideh Firoozbakht_, Aug 12 2006
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