A340306 - OEIS

%I #7 Jan 03 2021 22:42:25

%S 12,420,540,2268,7020,10692,11340,17640,24948,42750,56700,87120,

%T 152460,409500,413100,609840,996072,2478600,3822000,5287500,9189180,

%U 9447840,14871600,20241900,20567520,23510592,23832800,27766152,28552500,39358800,41135040,44783648,49985100

%N Numbers k such that A065642(k) = A081761(k).

%C Numbers k such that the least number that is larger than k and has the same prime signature as k and the least number that is larger than k and has the same set of distinct prime divisors as k are equal.

%H <a href="/index/Pri#prime_signature">Index entries for sequences related to prime signature</a>

%e 12 is a term since the A065642(12) = A081761(12) = 18, i.e., 18 = 2 * 3^2 is the least number with the same set of prime divisors, {2, 3}, and the same prime signature as 12 = 2^2 * 3.

%t 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]]; nextsig[n_] := Module[{sign = sig[n], k = n + 1}, While[sig[k] != sign, k++]; k]; Select[Range[2, 600], sig[#] == sig[next[#]] && rad[#] == rad[nextsig[#]] &]

%Y Intersection of A340302 and A340305.

%Y Cf. A065642, A081761.

%K nonn

%O 1,1

%A _Amiram Eldar_, Jan 03 2021