A396348 Array read by ascending antidiagonals: A(n,k) = prime(n)^A249344(n,k).

1, 2, 1, 1, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 9, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Comments

A(n,k) is the inverse of the prime(n)-adic absolute value of k.

References

Fernando Q. Gouvêa, p-Adic Numbers: An Introduction, Springer-Verlag, 2020; see pp. 34, 59.

Links

Table of n, a(n) for n=1..91.

Formula

Product_{n=1..oo} A(n,k) = k.

Example

The array begins as:
  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, ...
  2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, ...
  8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  2, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, ...
  ...

Mathematica

A[n_, k_]:=Prime[n]^IntegerExponent[k, Prime[n]]; Table[A[k, n - k + 1], {n, 1, 13}, {k, 1, n}]//Flatten

Crossrefs

Cf. A000040, A000961, A249344.

Columns give 1..5: A006519, A038500, A060904, A268354, A268357.

Rows 1..2 give: A000012, A054977.

Antidiagonal sum gives A396349.

Sequence in context: A337131 A046876 A026584 * A247342 A174547 A119326

Adjacent sequences: A396345 A396346 A396347 * A396349 A396350 A396351

Keyword

nonn,easy,tabl

Author

Stefano Spezia, May 23 2026

Status

approved