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A349213
a(n) = Sum_{d|n} n^((d+1) mod 2).
3
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Nov 10 2021
STATUS
approved