login
Numbers k such that the sum of unitary divisors of k is a cube.
2

%I #32 Mar 15 2020 03:22:51

%S 1,7,102,110,120,142,159,184,187,381,588,684,690,714,770,796,840,931,

%T 994,1034,1054,1065,1113,1128,1173,1240,1265,1288,1293,1309,1528,1633,

%U 1643,2619,2667,3638,3937,4280,4505,4664,4788,4830,4855,5176,5572,5671,5730

%N Numbers k such that the sum of unitary divisors of k is a cube.

%H Amiram Eldar, <a href="/A329239/b329239.txt">Table of n, a(n) for n = 1..10000</a>

%e 7 is a term since usigma(7) = 8 = 2^3, where usigma is A034448.

%e 102 is a term since usigma(102) = 216 = 6^3.

%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); Select[Range[10000], IntegerQ @ Surd[usigma [#], 3] &]

%o (PARI) isok(m) = ispower(sumdiv(m, d, if(gcd(d, m/d)==1, d)), 3); \\ _Michel Marcus_, Mar 15 2020

%Y The unitary version of A020477.

%Y Cf. A000578, A034448, A063937, A333258.

%K nonn

%O 1,2

%A _Amiram Eldar_, Mar 13 2020