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A113458 Least k such that k, k+n and k+2n have the same prime signature.

%I A113458 #10 Nov 05 2020 06:40:40
%S A113458 33,3,155,3,77,5,51,3,77,3,35,5,50,3,187,6,21,5,39,3,145,33,39,5,69,
%T A113458 39,91,3,33,7,15,12,221,3,28,7,21,3,55,3,33,5,91,66,209,69,35,5,50,3,
%U A113458 115,39,141,5,51,6,145,85,15,7,21,93,95,3,57,5,51,3,65,15,35,7,69,55,287,6
%N A113458 Least k such that k, k+n and k+2n have the same prime signature.
%C A113458 Third row of A113456.
%H A113458 Alois P. Heinz, <a href="/A113458/b113458.txt">Table of n, a(n) for n = 1..20000</a>
%e A113458 a(4) = 3 because 3, 7 and 11 have the same prime signature.
%p A113458 s:= n-> sort(map(i-> i[2], ifactors(n)[2])):
%p A113458 a:= proc(n) option remember; local k; for k
%p A113458       while s(k)<>s(k+n) or s(k)<>s(k+2*n) do od; k
%p A113458     end:
%p A113458 seq(a(n), n=1..100);  # _Alois P. Heinz_, Feb 28 2018
%t A113458 s[n_] := FactorInteger[n][[All, 2]] // Sort;
%t A113458 a[n_] := Module[{k}, For[k = 2, True, k++, If[s[k] == s[k+n] == s[k+2n], Return[k]]]];
%t A113458 Array[a, 100] (* _Jean-François Alcover_, Nov 05 2020 *)
%Y A113458 Cf. A052214, A113456, A113467.
%K A113458 easy,nonn
%O A113458 1,1
%A A113458 _David Wasserman_, Jan 08 2006