

A333258


Numbers k that are not powers of primes such that the sum of proper unitary divisors of k is a cube.


2



10, 12, 69, 122, 133, 153, 236, 363, 504, 752, 844, 992, 1001, 1018, 1243, 1685, 1819, 1940, 1994, 2295, 2323, 2619, 2871, 2900, 3184, 3403, 3483, 3641, 3763, 3981, 3984, 4024, 5482, 6471, 6892, 7128, 7925, 7928, 8186, 8856, 9077, 9352, 9641, 9664, 10113, 10404
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OFFSET

1,1


COMMENTS

Powers of primes are excluded since they are trivial terms: their sum of proper unitary divisors is 1 (except for 1 whose sum of proper unitary divisors is 0) .


LINKS

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


EXAMPLE

10 is a term since A034460(10) = 8 = 2^3.


MATHEMATICA

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


CROSSREFS

The unitary version of A048698.
Cf. A000961, A024619, A034448, A034460, A063936, A329239.
Sequence in context: A219917 A257039 A223150 * A241252 A301905 A167321
Adjacent sequences: A333255 A333256 A333257 * A333259 A333260 A333261


KEYWORD

nonn


AUTHOR

Amiram Eldar, Mar 13 2020


STATUS

approved



