A329393 Number of odd divisors minus number of even divisors of the n-th composite.

-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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..3000

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 *)
odmed[n_]:=With[{divs=Divisors[n]}, Count[divs, _?OddQ]-Count[divs, _?EvenQ]]; odmed/@Select[Range[100], CompositeQ] (* Harvey P. Dale, Nov 18 2024 *)

Crossrefs

Cf. A002808, A016825, A048272.

Sequence in context: A356707 A352938 A065861 * A336207 A344909 A126832

Adjacent sequences: A329390 A329391 A329392 * A329394 A329395 A329396

Keyword

sign

Author

Enrique Navarrete, Nov 12 2019

Status

approved