A340547 Square array, read by ascending antidiagonals, where row n gives all solutions n > 0 to A000120(n+1) = A000120((n+1)*k), A000120 is the Hamming weight.

1, 1, 2, 1, 2, 4, 1, 2, 3, 8, 1, 2, 4, 4, 16, 1, 2, 4, 8, 6, 32, 1, 2, 3, 8, 16, 8, 64, 1, 2, 3, 4, 13, 32, 11, 128, 1, 2, 4, 4, 6, 16, 64, 12, 256, 1, 2, 2, 8, 5, 8, 26, 128, 16, 512, 1, 2, 4, 8, 16, 6, 11, 32, 256, 22, 1024

Offset: 1

Author

Thomas Scheuerle, Jan 11 2021

Keywords

• nonn
• base
• tabl

Comments

Solutions to related equation A000120(k) = A000120(k*n) are A340351.

The same sequence without leading ones and only odd solutions is A340441.

Examples

			Eight initial terms of rows 1-8 are listed below:
   1: 1, 2, 4, 8, 16, 32, 64, 128, ...
   2: 1, 2, 3, 4,  6,  8, 11,  12, ...
   3: 1, 2, 4, 8, 16, 32, 64, 128, ...
   4: 1, 2, 4, 8, 13, 16, 26,  32, ...
   5: 1, 2, 3, 4,  6,  8, 11,  12, ...
   6: 1, 2, 3, 4,  5,  6,  7,   8, ...
   7: 1, 2, 4, 8, 16, 32, 64, 128, ...
   8: 1, 2, 4, 8, 16, 32, 57,  64, ...
T(3,4) = 8 because: (3+1) in binary is 100 and (3*1)*8 = 32 in binary is 100000, both have 1 bit set to 1.
		

Crossrefs

Cf. A000120, A340351, A340069, A340441.

Cf. A263132 (superset of 1st row), A007583 (1st row), A299960 (2nd row).

Formula

T(2n, ...) = 2^{0,1,2,...}, 2^{0,1,2,...} * row n of A340441.

T(4n+1, ...) = 2^{0,1,2,...}, 2^{0,1,2,...} * row n of A340441.

T(2^n, ...) = 2^{0,1,2,...}.