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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.

%I A340302 #9 Jan 06 2021 01:56:12
%S A340302 12,72,144,420,432,540,864,1728,1800,2000,2268,2520,2592,5184,5400,
%T A340302 6300,7020,10125,10368,10692,10800,11340,12600,15120,15552,16200,
%U A340302 17640,20000,20736,21168,21600,24000,24948,25200,26460,31104,37800,40500,41472,42750,43200
%N 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.
%C A340302 Numbers k such that A007947(k) = A007947(A081761(k)).
%C A340302 This sequence is infinite since it includes all the numbers of the form 2*6^k for k>=1.
%H A340302 Amiram Eldar, <a href="/A340302/b340302.txt">Table of n, a(n) for n = 1..500</a>
%H A340302 <a href="/index/Pri#prime_signature">Index entries for sequences related to prime signature</a>
%e A340302 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}.
%t A340302 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[#]] &]
%Y A340302 Cf. A007947, A081761, A085079, A089247, A118914, A167747.
%K A340302 nonn
%O A340302 1,1
%A A340302 _Amiram Eldar_, Jan 03 2021