A395042 Greatest prime dividing arithmetic derivative of n; and for primes p, a(p)=1.

1, 1, 2, 1, 5, 1, 3, 3, 7, 1, 2, 1, 3, 2, 2, 1, 7, 1, 3, 5, 13, 1, 11, 5, 5, 3, 2, 1, 31, 1, 5, 7, 19, 3, 5, 1, 7, 2, 17, 1, 41, 1, 3, 13, 5, 1, 7, 7, 5, 5, 7, 1, 3, 2, 23, 11, 31, 1, 23, 1, 11, 17, 3, 3, 61, 1, 3, 13, 59, 1, 13, 1, 13, 11, 5, 3, 71, 1, 11, 3, 43, 1, 31, 11, 5, 2, 7, 1, 41, 5, 3, 17, 7, 3, 17, 1, 11

Offset

2,3

Links

Antti Karttunen, Table of n, a(n) for n = 2..10000

Formula

a(n) = A006530(A003415(n)).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A395042(n) = A006530(A003415(n));

Crossrefs

Cf. A003415, A006530.

Cf. also A394895, A395052.

Sequence in context: A055205 A342001 A347957 * A377801 A369038 A161686

Adjacent sequences: A395039 A395040 A395041 * A395043 A395044 A395045

Keyword

nonn,easy

Author

Antti Karttunen, Apr 15 2026

Status

approved