A339549 a(n) is the product of the binary weights (A000120) of the divisors of n.

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

Offset: 1

Author

Amiram Eldar, Dec 08 2020

Keywords

• nonn
• base

Comments

Analogous to A093653 with product instead of sum.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000079, A000120, A093653.

Programs

Mathematica

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

PARI

a(n) = vecprod(apply(hammingweight, divisors(n))); \\ Michel Marcus, Dec 08 2020

Formula

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

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