OFFSET
0,13
LINKS
FORMULA
n = Product_{k=0..n} k^T(n, k). (Fundamental theorem of arithmetic.)
EXAMPLE
Triangle begins:
[ 0] 1;
[ 1] 0, 1;
[ 2] 0, 0, 1;
[ 3] 0, 0, 0, 1;
[ 4] 0, 0, 2, 0, 0;
[ 5] 0, 0, 0, 0, 0, 1;
[ 6] 0, 0, 1, 1, 0, 0, 0;
[ 7] 0, 0, 0, 0, 0, 0, 0, 1;
[ 8] 0, 0, 3, 0, 0, 0, 0, 0, 0;
[ 9] 0, 0, 0, 2, 0, 0, 0, 0, 0, 0;
[10] 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0;
MAPLE
Ord := proc(n, k)
if n = 0 then return 1 fi;
if n = 1 then return k fi;
if isprime(k) then padic:-ordp(n, k) else 0 fi end:
seq(seq(Ord(n, k), k = 0..n), n = 0..12);
MATHEMATICA
{{1}, {0, 1}}~Join~Table[If[PrimeQ[k], IntegerExponent[n, k], 0], {n, 2, 12}, {k, 0, n}] // Flatten (* Michael De Vlieger, May 11 2024 *)
PROG
(SageMath)
def T(n, k):
if n == 0: return 1
if n == 1: return k
return 0 if not is_prime(k) else n.valuation(k)
for n in srange(11): print([T(n, k) for k in range(n+1)])
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, May 11 2024
STATUS
approved