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

Author

Ilya Gutkovskiy, Nov 02 2020

Keywords

• nonn

Examples

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

Links

• Eric Weisstein's World of Mathematics, Unordered Factorization

Crossrefs

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

Programs

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}]

Formula

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