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

1,2

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A046755, A046754, A046756, A033950.

Sequence in context: A021173 A266553 A306980 * A346044 A334402 A227574

Adjacent sequences: A063918 A063919 A063920 * A063922 A063923 A063924

Keyword

nonn

Author

Labos Elemer, Sep 04 2001

Status

approved