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Date: 9-8-2020
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Date: 26-7-2020
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Date: 14-12-2019
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The unitary divisor function is the analog of the divisor function
for unitary divisors and denotes the sum-of-
th-powers-of-the-unitary divisors function. As in the case of the usual divisor function,
is commonly written
.
The numbers of unitary divisors is the same as the numbers of squarefree divisors of
, as well as
, where
is the number of different primes dividing
.
If is squarefree, then
.
can be computed using the formula
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which can be computed in the Wolfram Language as
UnitaryDivisorSigma[k_, n_Integer] := Times @@
(1 + (Power @@@ FactorInteger[n])^k)
The following table gives for
, 2, ... and small
.
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OEIS | ![]() ![]() |
0 | A034444 | 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, ... |
1 | A034448 | 1, 3, 4, 5, 6, 12, 8, 9, 10, 18, 12, 20, 14, 24, 24, ... |
2 | A034676 | 1, 5, 10, 17, 26, 50, 50, 65, 82, 130, 122, 170, 170, 250, 260, ... |
3 | A034677 | 1, 9, 28, 65, 126, 252, 344, 513, 730, 1134, 1332, 1820, ... |
4 | A034678 | 1, 17, 82, 257, 626, 1394, 2402, 4097, 6562, 10642, ... |
REFERENCES:
Sloane, N. J. A. Sequences A034444, A034448, A034676, A034677, and A034678 in "The On-Line Encyclopedia of Integer Sequences."
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