A345934 Ordinal transform of Kempner numbers, A002034.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jul 02 2021

Keywords

• nonn
• look

Comments

Number of values of k, 1 <= k <= n, with A002034(k) = A002034(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A002034, A345935.

Cf. also A344770.

Programs

Mathematica

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 *)

PARI

up_to = 65537;
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; };
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.
v345934 = ordinal_transform(vector(up_to,n,A002034(n)));
A345934(n) = v345934[n];

Formula

a(n) >= A345935(n).