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(Python)
from math import prod
from functools import reduce
from sympy import factorint
def A319687(n): return prod(sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin(p)[-1:2:-1], (1, 0)))**e for p, e in factorint(n).items())-sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin(n)[-1:2:-1], (1, 0))) # Chai Wah Wu, May 18 2023
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All terms seem to be even. See the conjecture given in A261179.