login
a(n) is the smallest multiple of n whose prime factorization exponents are all powers of 2.
9

%I #10 Jul 31 2022 07:46:36

%S 1,2,3,4,5,6,7,16,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,48,25,

%T 26,81,28,29,30,31,256,33,34,35,36,37,38,39,80,41,42,43,44,45,46,47,

%U 48,49,50,51,52,53,162,55,112,57,58,59,60,61,62,63,256,65,66,67

%N a(n) is the smallest multiple of n whose prime factorization exponents are all powers of 2.

%H Amiram Eldar, <a href="/A356194/b356194.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = n iff n is in A138302.

%t f[p_, e_] := p^(2^Ceiling[Log2[e]]); 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) = {my(f=factor(n)); prod(i=1, #f~, f[i,1]^s(f[i,2]))};

%Y Cf. A138302, A353897.

%Y Similar sequences: A053143, A053149, A053167, A066638, A087320, A087321, A197863, A356191, A356192, A356193.

%K nonn,easy,mult

%O 1,2

%A _Amiram Eldar_, Jul 29 2022