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A372330
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The number of divisors of the smallest multiple of n whose number of divisors is a power of 2 (A036537).
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1
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1, 2, 2, 4, 2, 4, 2, 4, 4, 4, 2, 8, 2, 4, 4, 8, 2, 8, 2, 8, 4, 4, 2, 8, 4, 4, 4, 8, 2, 8, 2, 8, 4, 4, 4, 16, 2, 4, 4, 8, 2, 8, 2, 8, 8, 4, 2, 16, 4, 8, 4, 8, 2, 8, 4, 8, 4, 4, 2, 16, 2, 4, 8, 8, 4, 8, 2, 8, 4, 8, 2, 16, 2, 4, 8, 8, 4, 8, 2, 16, 8, 4, 2, 16, 4
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OFFSET
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1,2
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COMMENTS
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Also, the number of infinitary divisors of the smallest multiple of n whose number of divisors is a power of 2.
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LINKS
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FORMULA
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Multiplicative with a(p^e) = 2^ceiling(log_2(e+1)).
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MATHEMATICA
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f[p_, e_] := 2^Ceiling[Log2[e + 1]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
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PROG
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(PARI) s(n) = {my(e=logint(n + 1, 2)); if(n + 1 == 2^e, n + 1, 2^(e+1))};
a(n) = {my(f=factor(n)); prod(i=1, #f~, s(f[i, 2]))};
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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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