A369760 The number of divisors of the smallest multiple of n whose prime factorization exponents are all powers of 2.

1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 10, 3, 4, 5, 6, 2, 8, 2, 9, 4, 4, 4, 9, 2, 4, 4, 10, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 10, 4, 10, 4, 4, 2, 12, 2, 4, 6, 9, 4, 8, 2, 6, 4, 8, 2, 15, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(A356194(n)).

Multiplicative with a(p^e) = 2^ceiling(log_2(e)) + 1.

a(n) >= A000005(n), with equality if and only if n is in A138302.

Mathematica

f[p_, e_] := 2^Ceiling[Log2[e]] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) s(n) = {my(e=logint(n, 2)); if(n == 2^e, n, 2^(e+1))};
a(n) = vecprod(apply(x -> s(x) + 1, factor(n)[, 2]));

Crossrefs

Cf. A000005, A138302, A353897, A356194, A369761, A369762.

Sequence in context: A333970 A338138 A384812 * A305899 A101296 A305898

Adjacent sequences: A369757 A369758 A369759 * A369761 A369762 A369763

Keyword

nonn,easy,mult

Author

Amiram Eldar, Jan 31 2024

Status

approved