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A367515
The number of unitary divisors of n that are exponentially odious numbers (A270428).
3
1, 2, 2, 2, 2, 4, 2, 1, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 4, 2, 2, 2, 4, 1, 4, 2, 8, 2, 1, 4, 4, 4, 4, 2, 4, 4, 2, 2, 8, 2, 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 2, 4, 2, 4, 4, 2, 8, 2, 4, 4, 1, 4, 8, 2, 4, 4, 8, 2, 2, 2, 4, 4, 4, 4, 8, 2, 4, 2, 4, 2, 8, 4, 4, 4
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = A001285(e).
a(n) = A034444(n)/A367516(n).
a(n) = 2^A293439(n).
a(n) >= 1, with equality if and only if n is an exponentially evil number (A262675).
a(n) <= A034444(n), with equality if and only if n is an exponentially odious number (A270428).
MATHEMATICA
f[p_, e_] := If[OddQ[DigitCount[e, 2, 1]], 2, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecprod(apply(x -> hammingweight(x)%2+1, factor(n)[, 2]));
(Python)
from sympy import factorint
def A367515(n): return 1<<sum(1 for e in factorint(n).values() if e.bit_count()&1) # Chai Wah Wu, Nov 23 2023
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Nov 21 2023
STATUS
approved