A328620 - OEIS

%I #11 Mar 13 2024 01:50:34

%S 0,0,1,0,1,0,2,1,1,0,1,0,2,1,1,0,1,0,2,1,1,0,1,0,2,1,1,0,1,0,3,2,2,1,

%T 2,1,2,1,1,0,1,0,2,1,1,0,1,0,2,1,1,0,1,0,2,1,1,0,1,0,3,2,2,1,2,1,2,1,

%U 1,0,1,0,2,1,1,0,1,0,2,1,1,0,1,0,2,1,1,0,1,0,3,2,2,1,2,1,2,1,1,0,1,0,2,1,1,0

%N Number of nonleading zeros in primorial base expansion of n, a(0) = 0 by convention.

%H Antti Karttunen, <a href="/A328620/b328620.txt">Table of n, a(n) for n = 0..32768</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.

%F a(n) = A001221(A328612(n)).

%F a(n) = A079067(A276086(n)).

%F a(A002110(n)) = n for all n >= 0.

%t a[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, If[r == 0, s++]; p = NextPrime[p]]; s]; Array[a, 100, 0] (* _Amiram Eldar_, Mar 13 2024 *)

%o (PARI) A328620(n) = { my(s=0, p=2); while(n, s += (0==(n%p)); n = n\p; p = nextprime(1+p)); (s); };

%Y Cf. A001221, A002110, A049345, A079067, A276086, A328612, A328614, A328615, A328616.

%Y Cf. A257510 for an analogous sequence.

%K nonn,base

%O 0,7

%A _Antti Karttunen_, Oct 23 2019