A323164 a(n) = A000720(A323075(n)).

0, 1, 2, 2, 3, 2, 4, 3, 4, 2, 5, 4, 6, 3, 5, 4, 7, 2, 8, 5, 5, 4, 9, 6, 5, 3, 8, 5, 10, 4, 11, 7, 9, 2, 10, 8, 12, 5, 8, 5, 13, 4, 14, 9, 11, 6, 15, 5, 14, 3, 10, 8, 16, 5, 11, 10, 8, 4, 17, 11, 18, 7, 14, 9, 16, 2, 19, 10, 15, 8, 20, 12, 21, 5, 10, 8, 19, 5, 22, 13, 11, 4, 23, 14, 15, 9, 17, 11, 24, 6, 22, 15, 14, 5, 19, 14, 25, 3, 19, 10, 26, 8, 27, 16, 20

Offset: 1

Author

Antti Karttunen, Jan 08 2019

Keywords

• nonn

Comments

One less than the restricted growth sequence transform of A323075.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000079, A000720, A000918, A323075, A323165 (ordinal transform).

Programs

Mathematica

A060681[n_] := n - If[1 == n, n, n/Min[FactorInteger[n][[All, 1]]]];
A323075[n_] := With[{nn = 1 + A060681[n]}, If[nn == n, n, A323075[nn]]];
a[n_] = PrimePi[A323075[n]];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022, from PARI code *)

PARI

A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));
A323075(n) = { my(nn = 1+A060681(n)); if(nn==n,n,A323075(nn)); };
A323164(n) = primepi(A323075(n));

Formula

a(n) = A000720(A323075(n)).

For all odd primes p, a(2^k * p - 2^(k+1) + 2) = a(A000079(k) * p - A000918(k+1)) = A000720(p) for k >= 0. - After David A. Corneth's similar observation for A323075.