A394884 - OEIS

%I #9 Apr 08 2026 15:21:51

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

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,2,1,1,1,1,

%U 1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N a(n) = A051903(A099308(n)), where A051903 is the maximum exponent in the prime factorization of n, and A099308 lists numbers m whose k-th arithmetic derivative is zero for some k.

%H Antti Karttunen, <a href="/A394884/b394884.txt">Table of n, a(n) for n = 1..12000</a>

%o (PARI)

%o A003415_checked(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 A051903(n) = if(n>1, vecmax(factor(n)[, 2]), 0)

%o is_A099308(n) = { while(n>1, n = A003415_checked(n)); (n); };

%o for(n=1,2^8,if(is_A099308(n),print1(A051903(n),", ")));

%Y Cf. A003415, A051903.

%Y Cf. A394885 (lists terms of A099308 that correspond to the records of this sequence).

%Y Cf. also A394886.

%K nonn

%O 1,7

%A _Antti Karttunen_, Apr 06 2026