A331295 Number of values of k, 1 <= k <= n, with f(k) = f(n), where f(n) = [A001222(n), A061395(n)].

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 3, 1, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 4, 2, 1, 1, 3, 3, 1, 2, 1, 1, 2, 1, 1, 3, 1, 3, 2, 1, 1, 2, 4, 1, 2, 1, 1, 5, 1, 4, 2, 1, 1, 4, 1, 1, 2, 3, 1, 2, 1, 1, 3, 4, 1, 2, 1, 3, 1, 1, 5, 3, 4, 1, 2, 1, 1, 6

Offset: 1

Author

Antti Karttunen, Jan 19 2020

Keywords

• nonn

Comments

Ordinal transform of A331298, or equally, of the ordered pair [A001222(n), A061395(n)].

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A001222, A061395, A078899, A331296, A331297, A331298.

Programs

Mathematica

f[n_] := f[n] = {PrimeOmega[n], PrimePi[FactorInteger[n]][[-1, 1]]};
a[n_] := Count[Array[f, n], f[n]];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022 *)

PARI

up_to = 1001;
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; };
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
Aux331298(n) = [bigomega(n), A061395(n)];
v331295 = ordinal_transform(vector(up_to, n, Aux331298(n)));
A331295(n) = v331295[n];