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A328959
a(n) = sigma_0(n) - 2 - (omega(n) - 1) * nu(n), where sigma_0 = A000005, nu = A001221, omega = A001222.
11
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
OFFSET
1,72
COMMENTS
Conjecture: All terms are nonnegative except for a(1) = -1.
FORMULA
a(n) = A000005(n) - A307408(n). - Antti Karttunen, Nov 17 2019
EXAMPLE
a(72) = sigma_0(72) - 2 - (omega(72) - 1) * nu(72) = 12 - 2 - (5 - 1) * 2 = 2.
MATHEMATICA
Table[DivisorSigma[0, n]-2-(PrimeOmega[n]-1)*PrimeNu[n], {n, 100}]
PROG
(PARI)
A307408(n) = 2+((bigomega(n)-1)*omega(n));
A328959(n) = (numdiv(n) - A307408(n)); \\ Antti Karttunen, Nov 17 2019
CROSSREFS
The positions of positive terms are conjectured to be A320632.
Positions of first appearances are A328963.
omega(n) * nu(n) is A113901(n).
(omega(n) - 1) * nu(n) is A307409.
sigma_0(n) - omega(n) * nu(n) is A328958(n).
Sequence in context: A185778 A071164 A027345 * A086080 A369054 A281477
KEYWORD
sign
AUTHOR
Gus Wiseman, Nov 02 2019. The idea for this sequence came from Mats Granvik.
STATUS
approved