A349211 a(n) = Sum_{d|n} d^((d+1) mod 2).

1, 3, 2, 7, 2, 10, 2, 15, 3, 14, 2, 26, 2, 18, 4, 31, 2, 29, 2, 38, 4, 26, 2, 58, 3, 30, 4, 50, 2, 52, 2, 63, 4, 38, 4, 81, 2, 42, 4, 86, 2, 68, 2, 74, 6, 50, 2, 122, 3, 65, 4, 86, 2, 84, 4, 114, 4, 62, 2, 148, 2, 66, 6, 127, 4, 100, 2, 110, 4, 100, 2, 185, 2, 78, 6, 122, 4

Offset

1,2

Comments

For each divisor d of n, add d if d is even. Otherwise add 1. For example, for n = 6, the divisors of 6 are 1, 2, 3, 6. This gives 1 + 2 + 1 + 6 = 10.

Links

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

Formula

a(p) = 2 iff p is an odd prime. - Wesley Ivan Hurt, Nov 28 2021

a(n) = A000005(A000265(n)) + A000203(A000265(n))*A000918(A001511(n)). - Chai Wah Wu, Jul 16 2022

Mathematica

Table[DivisorSum[n, #^Mod[(# + 1), 2] &], {n, 77}] (* Michael De Vlieger, Nov 10 2021 *)

Prog

(PARI) A349211(n) = sumdiv(n, d, d^((1+d)%2)); \\ Antti Karttunen, Dec 14 2021
(Python)
from math import prod
from sympy import factorint
def A349211(n):
    f = factorint(n>>(m:=(~n&n-1).bit_length())).items()
    d = prod(e+1 for p, e in f)
    s = prod((p**(e+1)-1)//(p-1) for p, e in f)
    return d+s*((1<<(m+1))-2) # Chai Wah Wu, Jul 16 2022

Crossrefs

Cf. A000005, A000203, A000265, A000918, A001511, A348915, A349213.

Sequence in context: A200593 A249112 A265219 * A266664 A308439 A245601

Adjacent sequences: A349208 A349209 A349210 * A349212 A349213 A349214

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 10 2021

Status

approved