A349212 a(n) = Sum_{d|n} n^(d mod 2).

1, 3, 6, 6, 10, 14, 14, 11, 27, 22, 22, 28, 26, 30, 60, 20, 34, 57, 38, 44, 84, 46, 46, 54, 75, 54, 108, 60, 58, 124, 62, 37, 132, 70, 140, 114, 74, 78, 156, 86, 82, 172, 86, 92, 270, 94, 94, 104, 147, 153, 204, 108, 106, 220, 220, 118, 228, 118, 118, 248, 122, 126, 378, 70, 260

Offset

1,2

Comments

For each divisor d of n, add n if d is odd, otherwise add 1. For example, 6 has 4 divisors 1,2,3,6 which gives a(6) = 6 + 1 + 6 + 1 = 14.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Christian Krause, et al, LODA, an assembly language, a computational model and a tool for mining integer sequences

Formula

a(n) = A000005(A001787(n)) = A001227(n) * (n+A007814(n)). [The first formula found by LODA miner] - Antti Karttunen, Apr 20 2022

Mathematica

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

Prog

(PARI) A349212(n) = sumdiv(n, d, n^(d%2)); \\ Antti Karttunen, Nov 10 2021
(Python)
from sympy import divisors
def a(n): return sum(n**(d%2) for d in divisors(n))
print([a(n) for n in range(1, 66)]) # Michael S. Branicky, Apr 20 2022
(Python)
from sympy import divisor_count
def A349212(n): return (n+(m:=(~n&n-1).bit_length()))*divisor_count(n>>m) # Chai Wah Wu, Jul 16 2022

Crossrefs

Cf. A000005, A001227, A001787, A007814, A349213, A348915.

Sequence in context: A276000 A333616 A316563 * A316140 A147849 A332546

Adjacent sequences: A349209 A349210 A349211 * A349213 A349214 A349215

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 10 2021

Status

approved