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A368885
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The number of unitary divisors of n that are squares of a squarefree number (A062503).
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2
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1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1
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OFFSET
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1,4
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COMMENTS
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First differs from A294932 at n = 32.
The largest of these divisors is A368884(n).
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LINKS
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FORMULA
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Multiplicative with a(p^e) = 2 if e = 2, and 1 otherwise.
a(n) >= 1, with equality if and only if n is in A337050.
Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + 1/p^(2*s) - 1/p^(3*s)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + 1/p^2 - 1/p^3) = 1.30596827416754083231... .
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MATHEMATICA
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f[p_, e_] := If[e == 2, 2, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
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PROG
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(PARI) a(n) = vecprod(apply(x->if(x==2, 2, 1), factor(n)[, 2]));
(Python)
from sympy import factorint
def A368885(n): return 1<<sum(1 for e in factorint(n).values() if e==2) # Chai Wah Wu, Jan 09 2024
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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