A373834 - OEIS

%I #12 Jun 21 2024 17:23:48

%S 1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,1,0,0,0,0,1,0,1,1,

%T 0,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,

%U 1,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1

%N a(n) = 1 if n is a multiple of A276150(n), otherwise 0, where A276150 is the digit sum in the primorial base.

%H Antti Karttunen, <a href="/A373834/b373834.txt">Table of n, a(n) for n = 0..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

%F For n >= 1, a(n) = [A373832(n) = 0], where [ ] is the Iverson bracket.

%F a(n) = A373851(A276086(n)).

%e a(0) = 1 because 0 is a multiple of A276150(0) = 0.

%e a(120) = 1 because 120 s a multiple of A276150(120) = 4.

%o (PARI)

%o A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };

%o A373834(n) = if(!n,1,!(n%A276150(n)));

%Y After the initial a(0)=1, characteristic function of A333426, primorial base Niven (or harshad) numbers: numbers divisible by their sum of digits in primorial base (A276150).

%Y Cf. A276086, A373832, A373833, A373851.

%K nonn

%O 0

%A _Antti Karttunen_, Jun 19 2024