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Numbers n such that digit sum of n equals digit sum of 'juxtaposition' and 'sum' of its prime factors (counted with multiplicity).
3

%I #10 Oct 10 2019 00:13:00

%S 4,22,27,94,121,166,202,265,274,346,355,382,438,454,517,526,562,634,

%T 706,852,913,915,922,1086,1111,1165,1219,1255,1282,1507,1626,1633,

%U 1642,1822,1894,1903,1966,2067,2155,2173,2182,2227,2265,2326,2362,2409,2434

%N Numbers n such that digit sum of n equals digit sum of 'juxtaposition' and 'sum' of its prime factors (counted with multiplicity).

%t d[n_]:=IntegerDigits[n]; co[n_,k_]:=Nest[Flatten[d[{#,n}]]&,n,k-1]; t={}; Do[If[!PrimeQ[n]&&Total[d[n]]==Total[d[Total[Times@@@(x=FactorInteger[n])]]]==Total[Flatten[d[co@@@x]]],AppendTo[t,n]],{n,4,2435}]; t (* _Jayanta Basu_, Jun 04 2013 *)

%Y Cf. A006753, A036920, A019506.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Jan 04 1999