OFFSET
1,1
COMMENTS
It is conjectured that there are no further terms. This was checked up to 2^21.
If x > 3 is an element of the sequence and y := (x-1)/2 is odd, then y is an element of the sequence. Because if y > 1 is a product of n factors (2 + 1/t_k) with integers t_k > 1, then x = 2*y + 1 = y * (2 + 1/y) is a product of n+1 such factors.
EXAMPLE
1 is not a term because the empty product has the value 1.
Other odd numbers that are not terms:
5 = (2 + 1/3) * (2 + 1/7);
9 = (2 + 1/9) * (2 + 1/ 13) * (2 + 1/19);
11 = (2 + 1/3) * (2 + 1/5) * (2 + 1/7);
17 = (2 + 1/25) * (2 + 1/27) * (2 + 1/37) * (2 + 1/55);
255 = (2 + 1/3)^4 * (2 + 1/7) * (2 + 1/139) * (2 + 1/10633).
PROG
(PARI) \\ Using the function nTuples from the linked file in A355626 and setting the global variable s:
s = 2; L = vector(3815); for (n = 2, 9, forstep (k = 2^n+1, (5/2)^n, 2, my (istup=nTuples(n, k, 1, 0)); if(istup, L[k]++))); forstep (k=2^10+1, 2^11-1, 2, my (istup=nTuples(10, k, 1, 0)); if(istup, L[k]++)); forstep (k=3, 2048, 2, if(L[k]==0, print1(k, ", ")));
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Hugo Pfoertner and Markus Sigg, Aug 16 2022
STATUS
approved