A136724 Numbers divisible by 4 that are not powers of 2.

12, 20, 24, 28, 36, 40, 44, 48, 52, 56, 60, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248

Offset: 1

Author

Artur Jasinski, Jan 19 2008

Keywords

• nonn

Comments

Primitive dimensions of Hadamard matrices which cannot be obtained as tensor powers of the primitive matrix 2 X 2 {{1,1},{1,-1}}.

5+7=12=2+4+6, 9+11=20=2+4+6+8,.. Numbers that can be expressed as sum of two or more positive consecutive odd numbers AND as sums of two or more positive consecutive even numbers. - Vladimir Joseph Stephan Orlovsky, May 11 2010

Numbers in A008586 but not in A000079. - Michel Marcus, Nov 07 2013

Nicomachus called these numbers "odd-times even". - Eric M. Schmidt, Mar 30 2019

Links

• Nicomachus, Introduction to Arithmetic, Book I, Chapter X.

Crossrefs

Cf. A007299.

Cf. A000079, A008586.

Programs

Mathematica

a = {}; Do[k = 4n; If[Round[Log[k]/Log[2]] == Log[k]/Log[2],[null], AppendTo[a, k]], {n, 1, 100}]; a
Select[Range[62]*4,!IntegerQ[Log2[#]]&] (* James C. McMahon, Jun 01 2025 *)