

A063921


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


1



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
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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 * A334402 A227574 A214869
Adjacent sequences: A063918 A063919 A063920 * A063922 A063923 A063924


KEYWORD

nonn


AUTHOR

Labos Elemer, Sep 04 2001


STATUS

approved



