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A345934 Ordinal transform of Kempner numbers, A002034.

%I A345934 #15 Jul 06 2021 18:26:01
%S A345934 1,1,1,1,1,2,1,2,1,2,1,3,1,2,3,2,1,3,1,4,3,2,1,4,1,2,1,4,1,5,1,1,3,2,
%T A345934 5,4,1,2,3,6,1,6,1,4,5,2,1,6,1,2,3,4,1,2,5,7,3,2,1,7,1,2,8,2,5,6,1,4,
%U A345934 3,9,1,7,1,2,3,4,7,6,1,8,3,2,1,10,5,2,3,8,1,9,7,4,3,2,5,3,1,2,9,4,1,6,1,8,11
%N A345934 Ordinal transform of Kempner numbers, A002034.
%C A345934 Number of values of k, 1 <= k <= n, with A002034(k) = A002034(n).
%H A345934 Antti Karttunen, <a href="/A345934/b345934.txt">Table of n, a(n) for n = 1..65537</a>
%H A345934 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A345934 a(n) >= A345935(n).
%t A345934 Table[Length@Select[Table[m=1;While[Mod[m!,k]!=0,m++];m,{k,n}],#==(m=1;While[Mod[m!,n]!=0,m++];m)&],{n,100}] (* _Giorgos Kalogeropoulos_, Jul 03 2021 *)
%o A345934 (PARI)
%o A345934 up_to = 65537;
%o A345934 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 A345934 A002034(n) = if(1==n,n,my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.
%o A345934 v345934 = ordinal_transform(vector(up_to,n,A002034(n)));
%o A345934 A345934(n) = v345934[n];
%Y A345934 Cf. A002034, A345935.
%Y A345934 Cf. also A344770.
%K A345934 nonn,look
%O A345934 1,6
%A A345934 _Antti Karttunen_, Jul 02 2021