A323164 - OEIS

%I #15 Jan 10 2022 06:51:47

%S 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,

%T 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,

%U 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

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

%C One less than the restricted growth sequence transform of A323075.

%H Antti Karttunen, <a href="/A323164/b323164.txt">Table of n, a(n) for n = 1..65537</a>

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

%F 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.

%t A060681[n_] := n - If[1 == n, n, n/Min[FactorInteger[n][[All, 1]]]];

%t A323075[n_] := With[{nn = 1 + A060681[n]}, If[nn == n, n, A323075[nn]]];

%t a[n_] = PrimePi[A323075[n]];

%t Array[a, 105] (* _Jean-François Alcover_, Jan 10 2022, from PARI code *)

%o (PARI)

%o A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));

%o A323075(n) = { my(nn = 1+A060681(n)); if(nn==n,n,A323075(nn)); };

%o A323164(n) = primepi(A323075(n));

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

%K nonn

%O 1,3

%A _Antti Karttunen_, Jan 08 2019