|
|
A353068
|
|
Irregular triangle read by rows: T(n,k) = n - multiplicity of prime(k) as a divisor of n!.
|
|
1
|
|
|
1, 2, 2, 1, 3, 2, 4, 4, 2, 4, 5, 3, 5, 6, 6, 1, 6, 7, 7, 2, 5, 8, 8, 2, 6, 8, 9, 3, 7, 9, 10, 10, 2, 7, 10, 11, 11, 3, 8, 11, 12, 12, 12, 3, 9, 12, 12, 13, 13, 4, 9, 12, 13, 14, 14, 1, 10, 13, 14, 15, 15, 2, 11, 14, 15, 16, 16, 16, 2, 10, 15, 16, 17, 17, 17, 3, 11, 16, 17, 18, 18, 18, 18
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,2
|
|
COMMENTS
|
This is the "s" in the American Mathematical Monthly problem.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
First few rows are:
1;
2, 2;
1, 3;
2, 4, 4;
2, 4, 5;
3, 5, 6, 6;
1, 6, 7, 7;
2, 5, 8, 8;
2, 6, 8, 9;
3, 7, 9, 10, 10;
2, 7, 10, 11, 11;
...
|
|
MATHEMATICA
|
T[n_, k_] := n - IntegerExponent[n!, Prime[k]]; Table[T[n, k], {n, 2, 19}, {k, 1, PrimePi[n]}] // Flatten (* Amiram Eldar, Apr 21 2022 *)
|
|
PROG
|
(PARI) row(n) = vector(primepi(n), k, n-valuation(n!, prime(k)));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|