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A353329 Number of divisors d of n for which A332823(d) is negative (-1). 9
0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 1, 2, 2, 1, 0, 3, 1, 1, 1, 2, 1, 2, 0, 2, 1, 1, 1, 3, 1, 1, 2, 2, 0, 3, 1, 2, 2, 1, 0, 3, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 0, 4, 1, 1, 2, 2, 1, 2, 0, 2, 1, 2, 1, 4, 0, 1, 2, 2, 1, 3, 1, 3, 2, 1, 0, 4, 1, 1, 2, 2, 1, 4, 2, 2, 1, 1, 1, 4, 0, 2, 2, 3, 1, 2, 0, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,12
COMMENTS
Number of divisors of n such that A048673(d) == -1 (mod 3).
LINKS
FORMULA
a(n) = Sum_{d|n} [A332823(d) < 0], where [ ] is the Iverson bracket, giving 1 only if A332823 computed for the divisor d is strictly negative, and 0 otherwise.
a(n) = A353328(n) - A353354(n).
a(n) = A353351(n) - A353328(n).
a(n) = A353328(A003961(n)).
PROG
(PARI)
A332823(n) = { my(f = factor(n), u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u, -1, u); };
A353329(n) = sumdiv(n, d, (A332823(d)<0));
CROSSREFS
Cf. A353355 [a(n) == A353328(n)], A353356 [a(n) < A353328(n)], A353357 [a(n) > A353328(n)].
Sequence in context: A025924 A025904 A137993 * A282778 A342788 A059883
KEYWORD
nonn
AUTHOR
Antti Karttunen and Peter Munn, Apr 16 2022
STATUS
approved

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)