OFFSET
1,1
COMMENTS
For n = 16, k^16 - 16 = (k^8 - 4)(k^8 + 4) = (k^4 - 2)(k^4 + 2)(k^8 + 4) always has at least three factors, so a(16) = 0. Similarly for any n of the form (2m)^4, so a(A016744(n)) = 0.
LINKS
Kevin P. Thompson, Table of n, a(n) for n = 1..115
Kevin P. Thompson, Table of n, a(n) for n = 1..154 with uncertain values
EXAMPLE
For n = 3:
k = 1: 1^3 - 3 = -2 < 0 so ignore.
k = 2: 2^3 - 3 = 5 which is not semiprime.
k = 3: 3^3 - 3 = 24 = 2 * 2 * 2 * 3 which is not semiprime.
k = 4: 4^3 - 3 = 61 which is not semiprime.
k = 5: 5^3 - 3 = 122 = 2 * 61 which is semiprime.
Therefore, a(3) = 5 since k = 5 is the first value for which k^3 - 3 is semiprime.
CROSSREFS
KEYWORD
nonn
AUTHOR
Kevin P. Thompson, Jun 12 2023
STATUS
approved