This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
for(n = 0, 100, print1(omega(12^n + 1), ", "))
EulerPhi[12^Range[0,19] + 1] (* Paul F. Marrero Romero, Oct 27 2023 *)
{a(n) = eulerphi(12^n+1)}
a(4)=21060 because 12^4+1 has divisors {1, 89, 233, 20737}.
a:=n->numtheory[sigma](12^n+1): seq(a(n), n=0..100);
a(4)=4 because 11^4+1 has divisors {1, 2, 7321, 14642}.
a:=n->numtheory[tau](11^n+1): seq(a(n), n=0..100);
DivisorSigma[0,11^Range[0,70]+1] (* Harvey P. Dale, Mar 17 2025 *)
a(n) = numdiv(11^n+1);
a(3)=4 because 4^3+1 has divisors {1, 5, 13, 65}.
a:=n->numtheory[tau](4^n+1): seq(a(n), n=0..100);
DivisorSigma[0,4^Range[0,100]+1] (* Paolo Xausa, Oct 14 2023 *)
a(n) = numdiv(4^n+1);
from sympy import divisor_count def A366606(n): return divisor_count((1<<(n<<1))+1) # Chai Wah Wu, Oct 14 2023
Table[FactorInteger[12^n + 1][[1,1]], {n, 0, 69}] (* Paul F. Marrero Romero, Oct 25 2023 *)
a(3)=12 because 5^3+1 has divisors {1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126}.
a:=n->numtheory[tau](5^n+1): seq(a(n), n=0..100);
DivisorSigma[0, 5^Range[0, 70] + 1] (* Paolo Xausa, Apr 20 2025 *)
a(n) = numdiv(5^n+1);
a(3)=4 because 6^3+1 has divisors {1, 7, 31, 217}.
a:=n->numtheory[tau](6^n+1): seq(a(n), n=0..100);
DivisorSigma[0, 6^Range[0, 70] + 1] (* Paolo Xausa, Apr 19 2025 *)
a(n) = numdiv(6^n+1);
a(4)=4 because 7^4+1 has divisors {1, 2, 1201, 2402}.
a:=n->numtheory[tau](7^n+1): seq(a(n), n=0..100);
DivisorSigma[0, 7^Range[0, 62] + 1] (* Paul F. Marrero Romero, Oct 16 2023 *)
a(n) = numdiv(7^n+1);
a(4)=4 because 8^4+1 has divisors {1, 17, 241, 4097}.
a:=n->numtheory[tau](8^n+1): seq(a(n), n=0..100);
DivisorSigma[0, 8^Range[0,59] + 1] (* Paul F. Marrero Romero, Nov 12 2023 *)
a(n) = numdiv(8^n+1);