A331296 Number of values of k, 1 <= k <= n, with A263297(k) = A263297(n), where A263297(n) = max(A001222(n), A061395(n)).

1, 1, 1, 2, 1, 3, 1, 2, 4, 3, 1, 4, 1, 2, 5, 3, 1, 6, 1, 7, 4, 2, 1, 5, 8, 2, 9, 6, 1, 10, 1, 3, 4, 2, 7, 8, 1, 2, 3, 9, 1, 10, 1, 5, 11, 2, 1, 6, 11, 12, 3, 4, 1, 12, 7, 13, 3, 2, 1, 14, 1, 2, 15, 5, 6, 8, 1, 4, 3, 16, 1, 9, 1, 2, 13, 4, 10, 7, 1, 11, 17, 2, 1, 18, 5, 2, 3, 12, 1, 19, 8, 4, 3, 2, 5, 9, 1, 20, 13, 21, 1, 6, 1, 10, 22

Offset: 1

Author

Antti Karttunen, Jan 18 2020

Keywords

• nonn

Comments

Ordinal transform of A263297.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A001222, A061395, A263297.

Cf. also A078899.

Programs

Mathematica

A263297[n_] := If[n == 1, 0, With[{f = FactorInteger[n]}, Max[PrimePi[Max[f[[All, 1]]]], Total[f[[All, 2]]]]]];
b[_] = 0;
a[n_] := With[{t = A263297[n]}, b[t] = b[t] + 1];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022 *)

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; };
A263297(n) = if(n<2, 0,  my(f=factor(n)); max(vecsum(f[, 2]), primepi(f[#f~, 1]))); \\ From A263297
v331296 = ordinal_transform(vector(up_to, n, A263297(n)));
A331296(n) = v331296[n];