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A071966
Composite numbers such that smallest prime factor, largest prime factor and sum of prime factors (with repetition) are all a sum of two squares.
1
4, 16, 20, 25, 30, 32, 52, 65, 78, 80, 90, 130, 145, 148, 156, 164, 169, 174, 200, 238, 240, 244, 250, 256, 265, 270, 272, 286, 289, 290, 300, 306, 318, 320, 340, 348, 360, 388, 400, 408, 436, 442, 450, 452, 455, 464, 480, 481, 505, 512, 522, 540, 546, 574
OFFSET
1,1
LINKS
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
Cf. A001481, A001414 (sopfr), A006530 (gpf), A020639 (spf), A002808 (composites).
Sequence in context: A280844 A277887 A216033 * A349521 A326781 A326788
KEYWORD
nonn
AUTHOR
Jason Earls, Jun 15 2002
STATUS
approved