A384232 Smallest number whose largest odd noncomposite divisor is its n-th divisor.

1, 3, 6, 20, 42, 84, 156, 312, 684, 1020, 1380, 1860, 3480, 3720, 4920, 7320, 10980, 14640, 16920, 21960, 26280, 34920, 45720, 59640, 69840, 89880, 106680, 125160, 145320, 177240, 213360, 244440, 269640, 354480, 320040, 375480, 435960, 456120, 531720, 647640, 708120

Offset: 1

Author

Omar E. Pol, May 23 2025

Keywords

• nonn

Comments

This coincide with A087134 except for the second term because here a(2) = 3 and there A087134(2) = 2.

Examples

			The divisors of 42 are [1, 2, 3, 6, 7, 14, 21, 42] and the largest odd noncomposite divisor is 7 and 7 is its 5th divisor, so a(5) = 42 because 42 the smallest number having that property.
		

Crossrefs

Row 1 of A384233.

Companion of A383402.

Cf. A006005, A027750, A087134.

Programs

Mathematica

With[{t = Table[FirstPosition[Divisors[n], FactorInteger[n/2^IntegerExponent[n, 2]][[-1, 1]]][[1]], {n, 1, 10^6}]}, TakeWhile[FirstPosition[t, #] & /@ Range[Max[t]] // Flatten, ! MissingQ[#] &]] (* Amiram Eldar, May 23 2025 *)