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

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..75.

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.

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

Sequence in context: A308605 A107748 A338506 * A005884 A229913 A285326

Adjacent sequences: A353187 A353188 A353189 * A353191 A353192 A353193

Keyword

nonn

Author

Omar E. Pol, Apr 29 2022

Status

approved