%I #22 Mar 21 2022 13:32:06
%S 2,3,5,7,250,735,792,2500,4992,9075,11760,25000,30625,67914,91476,
%T 117600,185625,187278,250000,264992,523908,630784,855360,1082565,
%U 1176000,2395008,2500000,2546775,2898350,3608550,3833280,4299750,4790016,5899068,8553600,9243850
%N Numbers n such that sum of the squares of the prime factors of n equals the sum of the squares of the digits of n.
%C From _David A. Corneth_, Sep 28 2019: (Start)
%C If 10*m is in the sequence then so is 100*m.
%C The sum of squares of digits of a k-digit number is at most 81*k. Therefore any term with at most k digits is p-smooth where p is the largest prime < (81*k)^(1/2). (End)
%H David A. Corneth, <a href="/A067184/b067184.txt">Table of n, a(n) for n = 1..14898</a> (terms < 10^20)
%e The prime factors of 4992 are 2,3,13, the sum of whose squares = 182 = sum of the squares of 4,9,9,2; so 4992 is a term of the sequence.
%t f[n_] := Module[{a, l, t, r}, a = FactorInteger[n]; l = Length[a]; t = Table[a[[i]][[1]], {i, 1, l}]; r = Sum[(t[[i]])^2, {i, 1, l}]]; g[n_] := Module[{b, m, s}, b = IntegerDigits[n]; m = Length[b]; s = Sum[(b[[i]])^2, {i, 1, m}]]; Select[Range[2, 10^5], f[ # ] == g[ # ] &]
%t Select[Range[2,4300000],Total[Transpose[FactorInteger[#]][[1]]^2]== Total[ IntegerDigits[#]^2]&] (* _Harvey P. Dale_, Sep 01 2011 *)
%Y Cf. A006753, A067170.
%K base,nonn
%O 1,1
%A _Joseph L. Pe_, Feb 18 2002
%E a(16)-a(32) from _Donovan Johnson_, Sep 29 2009
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