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A359166
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a(n) = lambda(n) * lambda(sigma(n)), where lambda is Liouville's lambda, and sigma is the sum of divisors function.
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4
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1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1
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OFFSET
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1
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LINKS
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FORMULA
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Multiplicative with a(p^e) = (-1)^(e + A001222(1 + p + p^2 + ... + p^e)).
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PROG
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(PARI) A359166(n) = ((-1)^(bigomega(n)+bigomega(sigma(n))));
(Python)
from functools import reduce
from operator import ixor
from collections import Counter
from sympy import factorint
def A359166(n): return (-1 if reduce(ixor, (f:=factorint(n)).values(), 0)&1 else 1)*(-1 if reduce(ixor, sum((Counter(factorint((p**(e+1)-1)//(p-1))) for p, e in f.items()), Counter()).values(), 0)&1 else 1) # Chai Wah Wu, Dec 23 2022
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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