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%I #7 Jan 06 2021 01:56:08
%S 12,45,60,63,84,132,156,175,204,228,275,276,315,325,348,350,372,420,
%T 425,444,475,492,495,516,525,539,540,564,575,585,636,637,660,675,693,
%U 700,708,732,765,780,804,819,833,852,855,876,924,931,948,996,1020,1035,1068
%N 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.
%C Numbers k such that k and A065642(k) have the same prime signature (A118914).
%H Amiram Eldar, <a href="/A340305/b340305.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#prime_signature">Index entries for sequences related to prime signature</a>
%e 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.
%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]]; Select[Range[2, 300], sig[#] == sig[next[#]] &]
%Y Cf. A065642, A118914.
%Y Subsequence: A251720.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jan 03 2021
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