A342004 a(n) = 1 if the maximal exponent in the prime factorization of the arithmetic derivative of n (A003415) is less than the maximal exponent in n, otherwise 0. a(1) = 1 by convention.

1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

a(n) = [A328311(n) == 0], where [ ] is the Iverson bracket.

For n > 1, a(n) = 1 if A342003(n) < A051903(n), otherwise 0.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A328311(n) = if(n<=1, 0, 1+(A051903(A003415(n)) - A051903(n)));
A342004(n) = (0==A328311(n));

Crossrefs

Characteristic function of A328320.

Cf. A003415, A051903, A328311, A342003, A342005.

Cf. also A341625, A341994, A341995, A341999.

Sequence in context: A342877 A140074 A351957 * A284881 A374048 A090174

Adjacent sequences: A342001 A342002 A342003 * A342005 A342006 A342007

Keyword

nonn

Author

Antti Karttunen, Mar 01 2021

Status

approved