A338568 Number of integers less than n with the same number of unordered factorizations as n.

0, 1, 2, 0, 3, 1, 4, 0, 2, 3, 5, 0, 6, 4, 5, 0, 7, 1, 8, 2, 6, 7, 9, 0, 8, 9, 1, 3, 10, 1, 11, 1, 10, 11, 12, 0, 12, 13, 14, 2, 13, 2, 14, 4, 5, 15, 15, 0, 16, 6, 17, 7, 16, 3, 18, 4, 19, 20, 17, 0, 18, 21, 8, 1, 22, 3, 19, 9, 23, 4, 20, 0, 21, 24, 10, 11, 25, 5, 22, 1

Offset

1,3

Links

Table of n, a(n) for n=1..80.

Eric Weisstein's World of Mathematics, Unordered Factorization

Formula

a(n) = |{j < n : A001055(j) = A001055(n)}|.

Example

a(10) = 3 because A001055(10) = 2 and also A001055(4) = A001055(6) = A001055(9) = 2.

Mathematica

T[_, 1] = T[1, _] = 1; T[n_, m_] := T[n, m] = DivisorSum[n, Boole[1 < # <= m] T[n/#, #] &]; A001055[n_] := T[n, n]; Table[Length[Select[Range[n - 1], A001055[#] == A001055[n] &]], {n, 80}]

Crossrefs

Cf. A001055, A330972 (positions of 0's), A338569.

Sequence in context: A241917 A355526 A243056 * A279119 A249738 A364020

Adjacent sequences: A338565 A338566 A338567 * A338569 A338570 A338571

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 02 2020

Status

approved