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%I #25 Jan 11 2022 08:33:13
%S 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 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 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 a(n) is the index of the column where n is located in array A277898, a(2) = 0.
%C a(2) = 0 as 2 does not occur in the array A277898 proper.
%C 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 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 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 A048675[n_] := If[n == 1, 0, Total[#[[2]]*2^(PrimePi[#[[1]]] - 1) & /@ FactorInteger[n]]];
%t A277892[n_] := PrimeOmega[A048675[n]];
%t Module[{b}, b[_] = 0;
%t a[n_] := If[n == 2, 0, With[{t = A277892[n]}, b[t] = b[t] + 1]]];
%t Table[a[n], {n, 2, 101}] (* _Jean-François Alcover_, Jan 11 2022 *)
%o (Scheme) (definec (A277895 n) (cond ((<= n 2) 0) ((= 1 (A010051 n)) 1) (else (+ 1 (A277895 (A277894 n))))))
%Y Cf. A010051, A277892, A277894, A277898, A277900.
%K nonn
%O 2,3
%A _Antti Karttunen_, Nov 08 2016
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