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A303759 Number of times the largest prime power factor of n (A034699) is largest prime power factor for numbers <= n; a(1) = 1.

%I A303759 #16 Jan 03 2022 11:13:51
%S A303759 1,1,1,1,1,2,1,1,1,2,1,2,1,2,3,1,1,2,1,4,3,2,1,2,1,2,1,4,1,5,1,1,3,2,
%T A303759 5,3,1,2,3,3,1,6,1,4,4,2,1,2,1,2,3,4,1,2,5,4,3,2,1,6,1,2,5,1,5,6,1,4,
%U A303759 3,7,1,6,1,2,3,4,7,6,1,3,1,2,1,8,5,2,3,8,1,7,7,4,3,2,5,2,1,2,9,4,1,6,1,8,9
%N A303759 Number of times the largest prime power factor of n (A034699) is largest prime power factor for numbers <= n; a(1) = 1.
%C A303759 Ordinal transform of A034699.
%H A303759 Antti Karttunen, <a href="/A303759/b303759.txt">Table of n, a(n) for n = 1..65537</a>
%p A303759 b:= proc() 0 end:
%p A303759 a:= proc(n) option remember; local t;
%p A303759       t:= max(1, seq(i[1]^i[2], i=ifactors(n)[2]));
%p A303759       b(t):= b(t)+1
%p A303759     end:
%p A303759 seq(a(n), n=1..120);  # _Alois P. Heinz_, Apr 30 2018
%t A303759 f[n_] := Max[Power @@@ FactorInteger[n]];
%t A303759 b[_] = 0;
%t A303759 a[n_] := With[{t = f[n]}, b[t] = b[t]+1];
%t A303759 Array[a, 105] (* _Jean-François Alcover_, Jan 03 2022 *)
%o A303759 (PARI)
%o A303759 up_to = 65537;
%o A303759 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 A303759 A034699(n) = if(1==n,n,fordiv(n, d, if(isprimepower(n/d), return(n/d))));
%o A303759 v303759 = ordinal_transform(vector(up_to,n,A034699(n)));
%o A303759 A303759(n) = v303759[n];
%Y A303759 Cf. A000961 (positions of ones), A034699.
%Y A303759 Cf. also A078899, A284600, A302789.
%K A303759 nonn
%O A303759 1,6
%A A303759 _Antti Karttunen_, Apr 30 2018