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

1,6

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

Formula

a(n) >= A345935(n).

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 *)

Prog

(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];

Crossrefs

Cf. A002034, A345935.

Cf. also A344770.

Sequence in context: A302776 A366510 A366522 * A060775 A355368 A175494

Adjacent sequences: A345931 A345932 A345933 * A345935 A345936 A345937

Keyword

nonn,look

Author

Antti Karttunen, Jul 02 2021

Status

approved