A394886 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.

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, 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, 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

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base.

Prog

(PARI)
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));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA099308(n) = { while(n>1, n = A003415checked(n)); (n); };
is_A328116(n) = isA099308(A276086(n));
A051903(n) = if(n>1, vecmax(factor(n)[, 2]), 0)
k=0; for(n=1, 2^8, if(is_A328116(n), print1(A051903(n), ", ")));

Crossrefs

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

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

Cf. also A394884.

Sequence in context: A202111 A187759 A358565 * A270645 A385234 A350239

Adjacent sequences: A394883 A394884 A394885 * A394887 A394888 A394889

Keyword

nonn

Author

Antti Karttunen, Apr 06 2026

Status

approved