(In reply to
Solution? by Jer)
Jer's prescription seemed so arbitrary that I couldn't believe it :-) So I tested it with odd numbers up to 999 and powers of 2 up to 14. The sorted (ascending) list of numbers that satisfy the prescription is listed below and is in complete agreement with Jer's result.
I imagine there is a way to exclude the possibility of any interloper being added to the list from a greater odd number, but I have stopped here. Program is
here.
coef n 2^n product
---------------------------
1 4 16 16
1 7 128 128
3 7 128 384
1 9 512 512
1 10 1024 1024
3 9 512 1536
7 8 256 1792
17 7 128 2176
5 9 512 2560
91 5 32 2912
3 10 1024 3072
5 10 1024 5120
7 10 1024 7168
1 13 8192 8192
9 10 1024 9216
11 10 1024 11264
13 10 1024 13312
15 10 1024 15360
61 8 256 15616
1 14 16384 16384
17 10 1024 17408
19 10 1024 19456
21 10 1024 21504
23 10 1024 23552
25 10 1024 25600
27 10 1024 27648
7 12 4096 28672
29 10 1024 29696
31 10 1024 31744
33 10 1024 33792
35 10 1024 35840
73 9 512 37376
37 10 1024 37888
39 10 1024 39936
41 10 1024 41984
339 7 128 43392
7 13 8192 57344
65 10 1024 66560
11 13 8192 90112
79 11 2048 161792
33 13 8192 270336
97 12 4096 397312
433 10 1024 443392
971 9 512 497152
579 11 2048 1185792
323 12 4096 1323008
955 11 2048 1955840
969 12 4096 3969024
479 14 16384 7847936
Edited on October 13, 2022, 11:42 pm
re: Solution? - confirmation
