A340305 Numbers k such that k and the least number that is larger than k and has the same set of distinct prime divisors as k also has the same prime signature as k.

12, 45, 60, 63, 84, 132, 156, 175, 204, 228, 275, 276, 315, 325, 348, 350, 372, 420, 425, 444, 475, 492, 495, 516, 525, 539, 540, 564, 575, 585, 636, 637, 660, 675, 693, 700, 708, 732, 765, 780, 804, 819, 833, 852, 855, 876, 924, 931, 948, 996, 1020, 1035, 1068

Offset: 1

Author

Amiram Eldar, Jan 03 2021

Keywords

• nonn

Comments

Numbers k such that k and A065642(k) have the same prime signature (A118914).

Examples

			12 is a term since the least number that is larger than 12 and has the same set of distinct prime divisors as 12, {2, 3}, is 18 = 2 * 3^2 which also has the same prime signature as 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to prime signature

Crossrefs

Cf. A065642, A118914.

Subsequence: A251720.

Programs

Mathematica

rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; next[n_] := Module[{r = rad[n]}, SelectFirst[Range[n + 1, n^2], rad[#] == r &]]; sig[n_] := Sort @ FactorInteger[n][[;; , 2]]; Select[Range[2, 300], sig[#] == sig[next[#]] &]