OFFSET
1,2
COMMENTS
Listed terms are 1, 2^2, 2^3, 3^2, 5^2, 3^3, 2^5, 6^2, 11^2, 5^3, 2^7, 52^2, 71^2 and 72^2.
It is observed that 4, 8, 25, 121 and 5041 are also terms of A227644 (Perfect powers equal to the sum of two factorial numbers), where in turn 25, 121 and 5041 are terms of A085692 (Brocard's problem), while the first 4 terms and 36 are part of A272575 (Perfect powers that are the sum of two Fibonacci numbers).
On the other hand, 4, 8, 32 and 128 are terms of A000079.
The representation for each term is as follows.
1 = 1! + 0
4 = 1! + 3 = 2! + 2
8 = 3! + 2
9 = 1! + 8 = 3! + 3
25 = 4! + 1
27 = 3! + 21 = 4! + 3
32 = 4! + 8
36 = 2! + 34
121 = 5! + 1
125 = 5! + 5
128 = 5! + 8
2704 = 5! + 2584
5041 = 7! + 1
5184 = 7! + 144
EXAMPLE
128 is a term because 128 = 2^7 and 128 = 5! + 8, where 8 is a Fibonacci number.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gonzalo MartÃnez, Mar 23 2024
STATUS
approved