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%I #13 Dec 05 2019 17:42:47
%S 4,16,20,25,30,32,52,65,78,80,90,130,145,148,156,164,169,174,200,238,
%T 240,244,250,256,265,270,272,286,289,290,300,306,318,320,340,348,360,
%U 388,400,408,436,442,450,452,455,464,480,481,505,512,522,540,546,574
%N Composite numbers such that smallest prime factor, largest prime factor and sum of prime factors (with repetition) are all a sum of two squares.
%H Amiram Eldar, <a href="/A071966/b071966.txt">Table of n, a(n) for n = 1..10000</a>
%e 481 is here since spf(481) = 13 = 2^2+3^2, lpf(481)= 37 = 1^2+6^2 and sopfr(481)= 50 = 1^2+7^2.
%t sumQ[n_] := AllTrue[FactorInteger[n], EvenQ[Last[#]] || Mod[First[#], 4]!=3 &]; aQ[n_] := CompositeQ[n] && AllTrue[{(f=FactorInteger[n])[[1,1]], f[[-1,1]], Plus @@ Times @@@ f}, sumQ]; Select[Range[574], aQ] (* _Amiram Eldar_, Dec 05 2019 *)
%Y Cf. A001481, A001414 (sopfr), A006530 (gpf), A020639 (spf), A002808 (composites).
%K nonn
%O 1,1
%A _Jason Earls_, Jun 15 2002