A394886 - OEIS

%I #10 Apr 06 2026 12:10:16

%S 0,1,1,2,1,1,1,2,2,1,2,1,2,1,1,5,1,1,1,1,3,1,1,1,2,2,2,1,1,1,2,1,1,1,

%T 2,1,2,1,1,1,1,2,3,1,4,1,1,2,1,1,1,1,2,2,1,2,2,1,1,2,1,1,2,1,1,2,1,1,

%U 2,1,1,1,1,4,1,2,5,1,1,3,1,3,1,1,8,1,1,2,1,2,1,2,1,1,1,1,1,2,1,1,1,1,1,1,2

%N a(n) = A051903(A328116(n)), where A051903 is the maximum exponent in the prime factorization of n,  and A328116 lists numbers m such that the k-th arithmetic derivative of A276086(m) is zero for some k.

%H Antti Karttunen, <a href="/A394886/b394886.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (PARI)

%o A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o isA099308(n) = { while(n>1, n = A003415checked(n)); (n); };

%o is_A328116(n) = isA099308(A276086(n));

%o A051903(n) = if(n>1, vecmax(factor(n)[, 2]), 0)

%o k=0; for(n=1,2^8,if(is_A328116(n),print1(A051903(n),", ")));

%Y Cf. A003415, A051903, A276086, A351256, A328116.

%Y Cf. A394887 (terms of A328116 that correspond to the records of this sequence).

%Y Cf. also A394884.

%K nonn

%O 1,4

%A _Antti Karttunen_, Apr 06 2026