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A175590 Numbers k with prime signature(k) = prime signature(k+1) = prime signature(k+2) = prime signature(k+3).

%I A175590 #22 May 11 2025 01:17:16
%S A175590 19940,49147,54585,118923,136825,183554,204323,204324,262932,304675,
%T A175590 361275,361322,476377,486962,506905,619722,668211,734948,854018,
%U A175590 937025,938203,999649,1062025,1118275,1335572,1336075,1356324,1466225,1541491
%N A175590 Numbers k with prime signature(k) = prime signature(k+1) = prime signature(k+2) = prime signature(k+3).
%H A175590 Charles R Greathouse IV, <a href="/A175590/b175590.txt">Table of n, a(n) for n = 1..10000</a>
%e A175590 a(1) = 2^2 * 5 * 997; a(1)+1 = 3 * 17^2 * 23; a(1)+2 = 2 * 13^2 * 59; a(1)+3 = 7^2 * 11 * 37. All have prime signature {2, 1, 1}.
%t A175590 SequencePosition[Table[Sort[FactorInteger[n][[All,2]]],{n,1542000}],{x_,x_,x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* The program will take a long time to run. *) (* _Harvey P. Dale_, Jun 09 2021 *)
%o A175590 (PARI) sig(n)={vecsort(factor(n)[,2])}; s=sig(1);for(n=1,1e6,t=sig(n+1);if(s==t&t==sig(n+2)&t==sig(n+3),print1(n-1,","));s=t)
%o A175590 (PARI) is_A175590(n)={my(f(n)=vecsort(factor(n)[,2]),t=f(n));!for(i=1,3,f(n+i)!=t & return)}  \\ _M. F. Hasler_, Nov 01 2012
%Y A175590 Cf. A052213, A052214, A218448. Subsequence of A070284.
%K A175590 nonn
%O A175590 1,1
%A A175590 _Charles R Greathouse IV_, Jul 19 2010