A394764 Maximum absolute difference over adjacent pairs in row n of A392091.

1, 3, 4, 6, 7, 9, 11, 12, 12, 13, 14, 16, 17, 17, 17, 18, 19, 21, 23, 24, 27, 30, 32, 34, 36, 39, 43, 47, 52, 57, 62, 67, 72, 77, 81, 85, 89, 93, 96, 99, 103, 107, 112, 118, 124, 130, 136, 142, 149, 156, 164, 172, 179, 186, 192, 198, 204, 210, 215, 220, 225, 231, 237, 243, 250

Offset

2,2

Comments

Let L = floor(log_2(n)), and let T(n,k) = A392091(n,k) for 1 <= k <= L. Consider the consecutive pairs (T(n,1),T(n,2)), (T(n,3),T(n,4)), ... . Then a(n) is the maximum of the absolute differences within these pairs; if L is odd, the final term is paired with 0. Since A380049(n) = Sum_{k=1..L} (-1)^(k-1)*T(n,k), a(n) is the largest absolute value among the pairwise contributions arising from these consecutive pairs in that alternating row sum.

Links

Table of n, a(n) for n=2..66.

Formula

Let L = floor(log_2(n)). Define U(n,k) = A392091(n,k) for 1 <= k <= L, and U(n,k) = 0 for k > L. Then a(n) = max_{1 <= r <= ceiling(L/2)} |U(n,2*r-1) - U(n,2*r)|.

Example

a(2) = 1 since row 2 of A392091 is (1), so the only pair is (1,0) and |1-0| = 1.
a(3) = 3 since row 3 of A392091 is (3), so the only pair is (3,0) and |3-0| = 3.
a(22) = 27 since row 22 of A392091 is (24,21,51,24), so the pair differences are |24-21| = 3 and |51-24| = 27, and the maximum is 27.

Mathematica

ClearAll[omega, T, a]; omega[n_] := Total[Last /@ FactorInteger[n]]; T[n_, k_] := Sum[Boole[omega[m] == k] (n - m + 1), {m, 2, n}]; a[n_] := Max[Table[Abs[T[n, r] - T[n, r + 1]], {r, 1, Floor[Log[2, n]], 2}]]; Table[a[n], {n, 2, 70}]

Crossrefs

Cf. A001222, A072203, A380049, A392091.

Sequence in context: A039026 A123540 A065313 * A382702 A103566 A258592

Adjacent sequences: A394761 A394762 A394763 * A394765 A394766 A394767

Keyword

nonn

Author

Tsuyoshi Hanatate, Mar 31 2026

Status

approved