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A369890 The number of divisors of the largest divisor of n whose exponents in its prime factorization are all powers of 2.

%I A369890 #29 Feb 16 2024 02:10:31
%S A369890 1,2,2,3,2,4,2,3,3,4,2,6,2,4,4,5,2,6,2,6,4,4,2,6,3,4,3,6,2,8,2,5,4,4,
%T A369890 4,9,2,4,4,6,2,8,2,6,6,4,2,10,3,6,4,6,2,6,4,6,4,4,2,12,2,4,6,5,4,8,2,
%U A369890 6,4,8,2,9,2,4,6,6,4,8,2,10,5,4,2,12,4,4
%N A369890 The number of divisors of the largest divisor of n whose exponents in its prime factorization are all powers of 2.
%C A369890 First differs from A369015 at n = 32.
%H A369890 Amiram Eldar, <a href="/A369890/b369890.txt">Table of n, a(n) for n = 1..10000</a>
%F A369890 a(n) = A000005(A353897(n)).
%F A369890 Multiplicative with a(p^e) = A053644(e) + 1.
%F A369890 a(n) = 2 if and only if n is prime.
%F A369890 a(n) <= A000005(n), with equality if and only if n is in A138302.
%t A369890 f[p_, e_] := 2^Floor[Log2[e]] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A369890 (PARI) a(n) = vecprod(apply(x -> 2^logint(x, 2) + 1, factor(n)[, 2]));
%Y A369890 Cf. A000005, A000079, A053644, A138302, A353897, A369015.
%K A369890 nonn,easy,mult
%O A369890 1,2
%A A369890 _Amiram Eldar_, Feb 15 2024