A354273 Square array read by ascending antidiagonals: A(n,k) = k^Omega(n).

1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 4, 3, 4, 1, 1, 2, 9, 4, 5, 1, 1, 4, 3, 16, 5, 6, 1, 1, 2, 9, 4, 25, 6, 7, 1, 1, 8, 3, 16, 5, 36, 7, 8, 1, 1, 4, 27, 4, 25, 6, 49, 8, 9, 1, 1, 4, 9, 64, 5, 36, 7, 64, 9, 10, 1, 1, 2, 9, 16, 125, 6, 49, 8, 81, 10, 11, 1, 1, 8, 3, 16, 25, 216, 7, 64, 9, 100, 11, 12, 1

Offset

1,5

Links

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

K. L. Verma, On an arithmetical functions involving general exponential, Palestine Journal of Mathematics Vol. 11(2)(2022), 496-504.

Formula

A(n, k) = A051129(A001222(n), k).

The columns are totally multiplicative: A(i*j, k) = A(i, k)*A(j, k).

Example

Array begins:
    1, 1,  1,  1,   1,   1,   1,   1, ...
    1, 2,  3,  4,   5,   6,   7,   8, ...
    1, 2,  3,  4,   5,   6,   7,   8, ...
    1, 4,  9, 16,  25,  36,  49,  64, ...
    1, 2,  3,  4,   5,   6,   7,   8, ...
    1, 4,  9, 16,  25,  36,  49,  64, ...
    1, 2,  3,  4,   5,   6,   7,   8, ...
    1, 8, 27, 64, 125, 216, 343, 512, ...
    ...

Mathematica

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

Crossrefs

Cf. A001222, A051129.

Cf. A000012 (n = 1 or k = 1), A061142 (k = 2), A165824 - A165871 (k = 3..50), A176029 (diagonal).

Sequence in context: A156041 A306210 A133255 * A282748 A145972 A215204

Adjacent sequences: A354270 A354271 A354272 * A354274 A354275 A354276

Keyword

nonn,tabl,easy

Author

Stefano Spezia, May 22 2022

Status

approved