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A363991
a(n) = Sum_{d|n, d odd} d^(d+1).
3
1, 1, 82, 1, 15626, 82, 5764802, 1, 3486784483, 15626, 3138428376722, 82, 3937376385699290, 5764802, 6568408355712906332, 1, 14063084452067724991010, 3486784483, 37589973457545958193355602, 15626, 122694327386105632949009377724, 3138428376722
OFFSET
1,3
FORMULA
G.f.: Sum_{k>0} (2*k-1)^(2*k) * x^(2*k-1) / (1 - x^(2*k-1)).
a(2^n) = 1.
MATHEMATICA
a[n_] := DivisorSum[n, #^(# + 1) &, OddQ[#] &]; Array[a, 22] (* Amiram Eldar, Jul 09 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d%2==1)*d^(d+1));
(Python)
from sympy import divisors
def A363991(n): return sum(d**(d+1) for d in divisors(n>>(~n & n-1).bit_length(), generator=True)) # Chai Wah Wu, Jul 09 2023
CROSSREFS
Cf. A364041.
Sequence in context: A347175 A352032 A051001 * A050678 A354501 A033402
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jul 09 2023
STATUS
approved