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(0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, ...) transform in (0*(1+2), 3*(2+2), 5*(2+3), 7*(2+3), 3*(2+2), 5*(11+2), 2*(3+13), ...).
1

%I #17 Jan 01 2017 15:46:55

%S 0,12,25,35,12,65,32,20,30,85,42,16,91,115,21,32,12,217,108,16,209,45,

%T 10,777,45,138,20,172,55,125,282,27,14,57,132,12,65,30,589,236,198,68,

%U 18,108,28,268,442,24,355,225,80,20,52,55,1053,32,172,332,36,765,93,300

%N (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, ...) transform in (0*(1+2), 3*(2+2), 5*(2+3), 7*(2+3), 3*(2+2), 5*(11+2), 2*(3+13), ...).

%H Michael De Vlieger, <a href="/A136739/b136739.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 0*(1+2) = 0;

%e a(2) = 3*(2+2) = 12;

%e a(3) = 5*(2+3) = 25;

%e a(4) = 7*(2+3) = 35;

%e a(5) = 3*(2+2) = 12;

%e a(6) = 5*(11+2) = 65;

%e a(7) = 2*(3+13) = 32;

%e a(8) = 2*(7+3) = 20; etc.

%t #1 (#2 + #3) & @@ # & /@ Partition[#, 3, 3] &@ Flatten[{0}~Join~Array[Map[If[Last@ # == 1, First@ #, #] &, FactorInteger@ #] &, 89]] (* _Michael De Vlieger_, Jan 01 2017 *)

%Y Cf. A141269, A141270.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Oct 31 2008

%E Entries checked by _R. J. Mathar_, Apr 25 2010