A394884 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.

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, 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, 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

Offset

1,7

Links

Antti Karttunen, Table of n, a(n) for n = 1..12000

Prog

(PARI)
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));
A051903(n) = if(n>1, vecmax(factor(n)[, 2]), 0)
is_A099308(n) = { while(n>1, n = A003415_checked(n)); (n); };
for(n=1, 2^8, if(is_A099308(n), print1(A051903(n), ", ")));

Crossrefs

Cf. A003415, A051903.

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

Cf. also A394886.

Sequence in context: A211111 A074971 A344008 * A198067 A282749 A132587

Adjacent sequences: A394881 A394882 A394883 * A394885 A394886 A394887

Keyword

nonn

Author

Antti Karttunen, Apr 06 2026

Status

approved