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A329393
Number of odd divisors minus number of even divisors of the n-th composite.
0
-1, 0, -2, 3, 0, -2, 0, 4, -3, 0, -2, 4, 0, -4, 3, 0, 4, -2, 0, -4, 4, 0, 4, -3, 0, 4, -4, 0, -2, 6, 0, -6, 3, 0, 4, -2, 0, 4, -4, 4, 0, -4, 0, 6, -5, 4, 0, -2, 4, 0, -6, 0, 6, -2, 4, 0, -6, 5, 0, -4, 4, 0, 4, -4, 0, 4, -2, 4, 0, 4, -8, 0, 6
OFFSET
1,3
COMMENTS
The mode, or most frequent value of this sequence is 0, which corresponds to composites with equal number of odd and even divisors, A016825(n), n >= 1. The next most frequent value is 4.
The value 2 does not appear in this sequence, in contrast to A048272, where A048272(p)=2 for every p = odd prime.
EXAMPLE
a(1) = -1 since the first composite number is 4, which has 1 odd divisor (1), and 2 even divisors (2,4).
a(2) = 0 since the second composite number is 6, which has 2 odd divisors (1,3) and 2 even divisors (2,6).
MATHEMATICA
f[p_, e_] := If[p == 2, 1 - e, 1 + e]; diffNum[1] = 1; diffNum[n_] := Times @@ (f @@@ FactorInteger[n]); diffNum /@ Select[Range[100], CompositeQ] (* Amiram Eldar, Nov 25 2019 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Enrique Navarrete, Nov 12 2019
STATUS
approved