A353190 a(n) is the (n-1)st odd number minus the sum of the aliquot parts of n.

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

Author

Omar E. Pol, Apr 29 2022

Keywords

• nonn

Comments

If n is a power of 2 then a(n) = n.

Note that A005408 has offset 0, hence A005408(0) = 1.

Examples

			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.
		

Crossrefs

Partial sums give A354801.

Cf. A000203, A000079, A001065, A005408, A016789.

Programs

Mathematica

a[n_] := 3*n - 1 - DivisorSigma[1, n]; Array[a, 75] (* Amiram Eldar, May 21 2022 *)

PARI

a(n) = 3*n-1-sigma(n); \\ Michel Marcus, May 04 2022

Formula

a(n) = A005408(n-1) - A001065(n).

a(n) = A016789(n-1) - A000203(n). - Michel Marcus, May 01 2022