A385757 a(n) is the smallest number having n smaller numbers with the same number of prime factors (counted with multiplicity).

3, 5, 7, 11, 13, 17, 19, 23, 26, 31, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205

Offset

1,1

Comments

a(n) is the least number k such that A335097(k) = n.

Links

Table of n, a(n) for n=1..65.

Eric Weisstein's World of Mathematics, Prime Factor.

Example

The smallest number having 9 smaller numbers (4, 6, 9, 10, 14, 15, 21, 22 and 25) with the same number of prime factors (counted with multiplicity) is 26, so a(9) is 26.

Mathematica

a[n_]:=Module[{k = 1, m, cnt}, While[True, m = PrimeOmega[k]; cnt = Sum[Boole[PrimeOmega[i] == m], {i, 2, k - 1}]; If[cnt == n, Return[k]]; k++ ]]; Array[a, 65] (* James C. McMahon, Jul 13 2025 *)

Prog

(PARI) a(n) = my(k=2, m=bigomega(k)); while (sum(i=2, k-1, bigomega(i) == m) !=n, k++; m=bigomega(k)); k; \\ Michel Marcus, Jul 09 2025

Crossrefs

Cf. A001222, A081376, A338483, A335097.

Sequence in context: A122089 A109860 A100392 * A309203 A176847 A067019

Adjacent sequences: A385754 A385755 A385756 * A385758 A385759 A385760

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 08 2025

Status

approved