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.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A071963 A071964 A071965 * A071967 A071968 A071969

Keyword

nonn

Author

Jason Earls, Jun 15 2002

Status

approved