A364037 Least number k such that the floor of the average of the distinct prime factors of k is n, or -1 if no such number exists.

2, 3, 14, 5, 22, 7, 39, 34, 38, 11, 46, 13, 115, 58, 62, 17, 155, 19, 111, 82, 86, 23, 94, 141, 235, 106, 159, 29, 118, 31, 183, 305, 134, 201, 142, 37, 219, 365, 158, 41, 166, 43, 415, 178, 267, 47, 623, 194, 291, 202, 206, 53, 214, 218, 327, 226, 339, 59, 791, 61

Offset: 2

Author

Jean-Marc Rebert, Jul 02 2023

Keywords

• nonn

Comments

All terms are squarefree. - Jon E. Schoenfield, Jul 02 2023

Examples

			a(4) = 14, because 14 = 2 * 7, floor((2 + 7) / 2) = 4, and no lesser number satisfies this.
		

Crossrefs

Cf. A363895.

Programs

Mathematica

seq[len_, kmax_] := Module[{s = Table[0, {len}], c = 0, k = 2, i}, While[c < len && k < kmax, i = Floor[Mean[FactorInteger[k][[;; , 1]]]] - 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = k]; k++]; s]; seq[60, 1000] (* Amiram Eldar, Jul 02 2023 *)

PARI

f(n) = my(p = factor(n)[, 1]); vecsum(p)\#p; \\ A363895
a(n) = my(k=2); while (f(k) != n, k++); k; \\ Michel Marcus, Jul 02 2023

Formula

a(p) = p for prime p. - David A. Corneth, Jul 02 2023