A063921 Quotients arising when A046755(n) is divided by the cube of the number of its divisors.

1, 5, 9, 1, 8, 1, 3, 343, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 16, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 16, 89, 97, 101, 103, 107, 109, 113, 6, 45, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 10, 211, 223, 227, 229, 64, 233, 239

Offset: 1

Author

Labos Elemer, Sep 04 2001

Keywords

• nonn

Examples

			Since (2^15)^p is in A046755 when p is a prime > 2, then p appears here at least once. Several terms breaking this regularity come from entries of A046755 of other categories. E.g. x=(2^10)*p*(11^3), d(x)=88, d(x)^3=(2^9)*(11^3) divides x and the quotient is 2p (p not equal to 11). Similar subsequences arise if 11 is replaced with different suitable primes.
		

Links

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

Crossrefs

Cf. A046755, A046754, A046756, A033950.

Programs

Magma

[k/#Divisors(k)^3:k in [m:m in [1..9000000]|IsIntegral(m/#Divisors(m)^3)]]; // Marius A. Burtea, Aug 07 2019

Mathematica

f[n_] := n/DivisorSigma[0, n]^3; Select[f /@ Range[10^5], IntegerQ] (* Amiram Eldar, Aug 07 2019 *)

Formula

a(n)= A046755(n)/(A000005(A046755(n))^3).