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A331296 Number of values of k, 1 <= k <= n, with A263297(k) = A263297(n), where A263297(n) = max(A001222(n), A061395(n)).

%I A331296 #10 Jan 10 2022 07:19:53
%S A331296 1,1,1,2,1,3,1,2,4,3,1,4,1,2,5,3,1,6,1,7,4,2,1,5,8,2,9,6,1,10,1,3,4,2,
%T A331296 7,8,1,2,3,9,1,10,1,5,11,2,1,6,11,12,3,4,1,12,7,13,3,2,1,14,1,2,15,5,
%U A331296 6,8,1,4,3,16,1,9,1,2,13,4,10,7,1,11,17,2,1,18,5,2,3,12,1,19,8,4,3,2,5,9,1,20,13,21,1,6,1,10,22
%N A331296 Number of values of k, 1 <= k <= n, with A263297(k) = A263297(n), where A263297(n) = max(A001222(n), A061395(n)).
%C A331296 Ordinal transform of A263297.
%H A331296 Antti Karttunen, <a href="/A331296/b331296.txt">Table of n, a(n) for n = 1..65537</a>
%H A331296 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%t A331296 A263297[n_] := If[n == 1, 0, With[{f = FactorInteger[n]}, Max[PrimePi[Max[f[[All, 1]]]], Total[f[[All, 2]]]]]];
%t A331296 b[_] = 0;
%t A331296 a[n_] := With[{t = A263297[n]}, b[t] = b[t] + 1];
%t A331296 Array[a, 105] (* _Jean-François Alcover_, Jan 10 2022 *)
%o A331296 (PARI)
%o A331296 up_to = 65537;
%o A331296 ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
%o A331296 A263297(n) = if(n<2, 0,  my(f=factor(n)); max(vecsum(f[, 2]), primepi(f[#f~, 1]))); \\ From A263297
%o A331296 v331296 = ordinal_transform(vector(up_to, n, A263297(n)));
%o A331296 A331296(n) = v331296[n];
%Y A331296 Cf. A001222, A061395, A263297.
%Y A331296 Cf. also A078899.
%K A331296 nonn
%O A331296 1,4
%A A331296 _Antti Karttunen_, Jan 18 2020