A369760 - OEIS

%I #8 Feb 03 2024 10:16:28

%S 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,

%T 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,

%U 2,6,4,8,2,15,2,4,6,6,4,8,2,10,5,4,2,12

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

%H Amiram Eldar, <a href="/A369760/b369760.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

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

%o (PARI) s(n) = {my(e=logint(n, 2)); if(n == 2^e, n, 2^(e+1))};

%o a(n) = vecprod(apply(x -> s(x) + 1, factor(n)[, 2]));

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

%K nonn,easy,mult

%O 1,2

%A _Amiram Eldar_, Jan 31 2024