A339549 - OEIS

%I #11 Dec 09 2020 01:14:29

%S 1,1,2,1,2,4,3,1,4,4,3,8,3,9,16,1,2,16,3,8,18,9,4,16,6,9,16,27,4,256,

%T 5,1,12,4,18,64,3,9,24,16,3,324,4,27,128,16,5,32,9,36,16,27,4,256,30,

%U 81,24,16,5,4096,5,25,216,1,12,144,3,8,24,324,4,256,3

%N a(n) is the product of the binary weights (A000120) of the divisors of n.

%C Analogous to A093653 with product instead of sum.

%H Amiram Eldar, <a href="/A339549/b339549.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Product_{d|n} A000120(d).

%F a(n) = 1 if and only if n is a power of 2 (A000079).

%e a(6) = 4 since the divisors of 6 are {1, 2, 3, 6}, and in binary representation {1, 10, 11, 110}. The number of 1's are {1, 1, 2, 2} and their product is 1*1*2*2 = 4.

%t a[n_] := Times @@ (DigitCount[#, 2, 1] & /@ Divisors[n]); Array[a, 100]

%o (PARI) a(n) = vecprod(apply(hammingweight, divisors(n))); \\ _Michel Marcus_, Dec 08 2020

%Y Cf. A000079, A000120, A093653.

%K nonn,base

%O 1,3

%A _Amiram Eldar_, Dec 08 2020