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A277895 a(n) is the index of the column where n is located in array A277898, a(2) = 0.

%I A277895 #25 Jan 11 2022 08:33:13
%S A277895 0,1,2,1,3,1,4,2,5,1,3,1,4,5,6,1,6,1,7,8,7,1,8,2,9,10,11,1,9,1,10,3,
%T A277895 12,4,13,1,14,15,11,1,12,1,5,6,13,1,16,2,17,7,18,1,14,8,15,9,3,1,10,1,
%U A277895 11,12,19,4,16,1,13,14,17,1,18,1,20,21,15,5,22,1,16,17,23,1,18,19,24,25,19,1,26,6,20,2,21,7,20,1,21,22,27,1
%N A277895 a(n) is the index of the column where n is located in array A277898, a(2) = 0.
%C A277895 a(2) = 0 as 2 does not occur in the array A277898 proper.
%C A277895 From a(3) onward the ordinal transform of A277892 from its first nonzero term a(3) onward: 1, 1, 2, 1, 3, 1, 2, 1, 4, 2, 5, 2, 2, 2, 6, 1, 7, 2, ... The relation does not hold the other way, because not all columns of A277898 are monotonic, for example, 16 is located below 18 in the sixth column of that array. Already the array's second column (A277900) is nonmonotonic.
%H A277895 Antti Karttunen, <a href="/A277895/b277895.txt">Table of n, a(n) for n = 2..10000</a> (computed from the b-file provided by _Hans Havermann_ for A277892)
%F A277895 a(2)=0, for n >= 3, if A010051(n) = 1 [when n is a prime], a(n) = 1, otherwise a(n) = 1 + a(A277894(n)).
%t A277895 A048675[n_] := If[n == 1, 0, Total[#[[2]]*2^(PrimePi[#[[1]]] - 1) & /@ FactorInteger[n]]];
%t A277895 A277892[n_] := PrimeOmega[A048675[n]];
%t A277895 Module[{b}, b[_] = 0;
%t A277895 a[n_] := If[n == 2, 0, With[{t = A277892[n]}, b[t] = b[t] + 1]]];
%t A277895 Table[a[n], {n, 2, 101}] (* _Jean-François Alcover_, Jan 11 2022 *)
%o A277895 (Scheme) (definec (A277895 n) (cond ((<= n 2) 0) ((= 1 (A010051 n)) 1) (else (+ 1 (A277895 (A277894 n))))))
%Y A277895 Cf. A010051, A277892, A277894, A277898, A277900.
%K A277895 nonn
%O A277895 2,3
%A A277895 _Antti Karttunen_, Nov 08 2016