A303759 - OEIS

%I #16 Jan 03 2022 11:13:51

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

%C Ordinal transform of A034699.

%H Antti Karttunen, <a href="/A303759/b303759.txt">Table of n, a(n) for n = 1..65537</a>

%p b:= proc() 0 end:

%p a:= proc(n) option remember; local t;

%p       t:= max(1, seq(i[1]^i[2], i=ifactors(n)[2]));

%p       b(t):= b(t)+1

%p     end:

%p seq(a(n), n=1..120);  # _Alois P. Heinz_, Apr 30 2018

%t f[n_] := Max[Power @@@ FactorInteger[n]];

%t b[_] = 0;

%t a[n_] := With[{t = f[n]}, b[t] = b[t]+1];

%t Array[a, 105] (* _Jean-François Alcover_, Jan 03 2022 *)

%o (PARI)

%o up_to = 65537;

%o 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 A034699(n) = if(1==n,n,fordiv(n, d, if(isprimepower(n/d), return(n/d))));

%o v303759 = ordinal_transform(vector(up_to,n,A034699(n)));

%o A303759(n) = v303759[n];

%Y Cf. A000961 (positions of ones), A034699.

%Y Cf. also A078899, A284600, A302789.

%K nonn

%O 1,6

%A _Antti Karttunen_, Apr 30 2018