A349213 a(n) = Sum_{d|n} n^((d+1) mod 2).

1, 3, 2, 9, 2, 14, 2, 25, 3, 22, 2, 50, 2, 30, 4, 65, 2, 57, 2, 82, 4, 46, 2, 146, 3, 54, 4, 114, 2, 124, 2, 161, 4, 70, 4, 219, 2, 78, 4, 242, 2, 172, 2, 178, 6, 94, 2, 386, 3, 153, 4, 210, 2, 220, 4, 338, 4, 118, 2, 484, 2, 126, 6, 385, 4, 268, 2, 274, 4, 284, 2, 651, 2, 150

Offset

1,2

Comments

For each divisor d of n, add n if d is even, otherwise add 1. For example, the divisors of 6 are 1,2,3,6 which would give a(6) = 1 + 6 + 1 + 6 = 14.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = A001227(n) * (1+n*A007814(n)). - Chai Wah Wu, Jul 16 2022

Mathematica

a[n_] := DivisorSum[n, n^Mod[# + 1, 2] &]; Array[a, 100] (* Wesley Ivan Hurt, Nov 12 2022 *)

Prog

(PARI) A349213(n) = sumdiv(n, d, n^((1+d)%2)); \\ Antti Karttunen, Nov 10 2021
(Python)
from sympy import divisor_count
def A349213(n): return (1+n*(m:=(~n&n-1).bit_length()))*divisor_count(n>>m) # Chai Wah Wu, Jul 16 2022

Crossrefs

Cf. A001227, A007814, A349211, A349212, A348915.

Sequence in context: A143074 A173624 A182023 * A228936 A169862 A245884

Adjacent sequences: A349210 A349211 A349212 * A349214 A349215 A349216

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 10 2021

Status

approved