A381279 a(1) = 1, for n > 1, a(n) = a(n - 1) / 2 if a(n - 1) is divisible by 2, otherwise a(n) = a(n - 1) + A000005(n - 1).

1, 2, 1, 3, 6, 3, 7, 9, 13, 16, 8, 4, 2, 1, 5, 9, 14, 7, 13, 15, 21, 25, 29, 31, 39, 42, 21, 25, 31, 33, 41, 43, 49, 53, 57, 61, 70, 35, 39, 43, 51, 53, 61, 63, 69, 75, 79, 81, 91, 94, 47, 51, 57, 59, 67, 71, 79, 83, 87, 89, 101, 103, 107, 113, 120, 60, 30, 15, 21, 25

Offset

1,2

Comments

a(n) = 1 for n from {1, 3, 14, 4636, 10213, 125331, ..}

Links

Table of n, a(n) for n=1..70.

Example

a(1) = 1.
a(2) = 1 + A000005(1) = 2.
a(3) = 2/2 = 1.
a(4) = 1 + A000005(3) = 3.
and so on.

Mathematica

a[1] = 1; a[n_] := a[n] = If[EvenQ[a[n-1]], a[n-1]/2, a[n-1] + DivisorSigma[0, n-1]]; Array[a, 100] (* Amiram Eldar, Apr 12 2025 *)

Crossrefs

Cf. A000005.

Sequence in context: A221918 A193897 A226122 * A347297 A133904 A245182

Adjacent sequences: A381276 A381277 A381278 * A381280 A381281 A381282

Keyword

nonn

Author

Ctibor O. Zizka, Apr 12 2025

Status

approved