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A353190
a(n) is the (n-1)st odd number minus the sum of the aliquot parts of n.
1
1, 2, 4, 4, 8, 5, 12, 8, 13, 11, 20, 7, 24, 17, 20, 16, 32, 14, 36, 17, 30, 29, 44, 11, 43, 35, 40, 27, 56, 17, 60, 32, 50, 47, 56, 16, 72, 53, 60, 29, 80, 29, 84, 47, 56, 65, 92, 19, 89, 56, 80, 57, 104, 41, 92, 47, 90, 83, 116, 11, 120, 89, 84, 64, 110, 53, 132, 77, 110, 65, 140, 20, 144, 107, 100
OFFSET
1,2
COMMENTS
If n is a power of 2 then a(n) = n.
Note that A005408 has offset 0, hence A005408(0) = 1.
FORMULA
a(n) = A005408(n-1) - A001065(n).
a(n) = A016789(n-1) - A000203(n). - Michel Marcus, May 01 2022
EXAMPLE
For n = 10, the first ten odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. The last of them is A005408(10-1) = 19. On the other hand the sum of the aliquot parts of 10 is 1 + 2 + 5 = 8, so a(10) = 19 - 8 = 11.
MATHEMATICA
a[n_] := 3*n - 1 - DivisorSigma[1, n]; Array[a, 75] (* Amiram Eldar, May 21 2022 *)
PROG
(PARI) a(n) = 3*n-1-sigma(n); \\ Michel Marcus, May 04 2022
CROSSREFS
Partial sums give A354801.
Sequence in context: A308605 A107748 A338506 * A005884 A229913 A285326
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 29 2022
STATUS
approved