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%I #10 Nov 23 2023 12:28:14
%S 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,
%T 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,
%U 4,8,2,2,2,4,4,4,4,8,2,4,2,4,2,8,4,4,4
%N The number of unitary divisors of n that are exponentially odious numbers (A270428).
%H Amiram Eldar, <a href="/A367515/b367515.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = A001285(e).
%F a(n) = A034444(n)/A367516(n).
%F a(n) = 2^A293439(n).
%F a(n) >= 1, with equality if and only if n is an exponentially evil number (A262675).
%F a(n) <= A034444(n), with equality if and only if n is an exponentially odious number (A270428).
%t f[p_, e_] := If[OddQ[DigitCount[e, 2, 1]], 2, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) a(n) = vecprod(apply(x -> hammingweight(x)%2+1, factor(n)[, 2]));
%o (Python)
%o from sympy import factorint
%o def A367515(n): return 1<<sum(1 for e in factorint(n).values() if e.bit_count()&1) # _Chai Wah Wu_, Nov 23 2023
%Y Cf. A001285, A262675, A270428, A293439.
%Y Similar sequences: A034444, A055076, A056624, A366901, A366902, A367516.
%K nonn,easy,mult
%O 1,2
%A _Amiram Eldar_, Nov 21 2023
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