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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 18 17:05 EDT 2024. Contains 375269 sequences. (Running on oeis4.)