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%I #20 Sep 08 2022 08:45:04
%S 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,
%T 67,71,73,79,83,16,89,97,101,103,107,109,113,6,45,127,131,137,139,149,
%U 151,157,163,167,173,179,181,191,193,197,199,10,211,223,227,229,64,233,239
%N Quotients arising when A046755(n) is divided by the cube of the number of its divisors.
%H Amiram Eldar, <a href="/A063921/b063921.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n)= A046755(n)/(A000005(A046755(n))^3).
%e 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.
%t f[n_] := n/DivisorSigma[0, n]^3; Select[f /@ Range[10^5], IntegerQ] (* _Amiram Eldar_, Aug 07 2019 *)
%o (Magma) [k/#Divisors(k)^3:k in [m:m in [1..9000000]|IsIntegral(m/#Divisors(m)^3)]]; // _Marius A. Burtea_, Aug 07 2019
%Y Cf. A046755, A046754, A046756, A033950.
%K nonn
%O 1,2
%A _Labos Elemer_, Sep 04 2001