A340302 Numbers k such that k and the least number that is larger than k and has the same prime signature as k also has the same set of distinct prime divisors as k.

12, 72, 144, 420, 432, 540, 864, 1728, 1800, 2000, 2268, 2520, 2592, 5184, 5400, 6300, 7020, 10125, 10368, 10692, 10800, 11340, 12600, 15120, 15552, 16200, 17640, 20000, 20736, 21168, 21600, 24000, 24948, 25200, 26460, 31104, 37800, 40500, 41472, 42750, 43200

Offset: 1

Author

Amiram Eldar, Jan 03 2021

Keywords

• nonn

Comments

Numbers k such that A007947(k) = A007947(A081761(k)).

This sequence is infinite since it includes all the numbers of the form 2*6^k for k>=1.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500
• Index entries for sequences related to prime signature

Crossrefs

Cf. A007947, A081761, A085079, A089247, A118914, A167747.

Programs

Mathematica

sig[n_] := Sort@FactorInteger[n][[;; , 2]]; nextsig[n_] := Module[{sign = sig[n], k = n + 1}, While[sig[k] != sign, k++]; k]; rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; Select[Range[2, 1000], rad[#] == rad[nextsig[#]] &]