OFFSET
1,1
COMMENTS
All terms are composite since sigma(p) = p + 1 and sigma(p^3) = p^3 + p^2 + p + 1 = (p + 1)(p^2 + 1) for p prime.
An odd number n with prime factorization Product_i p_i^(e_i) is in this sequence if and only if Product_i ((p_i^(3*e_i + 1) - 1)/(p_i^(e_i + 1) - 1)) is not an integer.
Nonsquare terms of this sequence are 27, 63, 75, 99, 117, 125, 135, 147, 153, 171, 175, 207, 243, 245, 261, 275, ...
Terms that are not perfect powers are 63, 75, 99, 117, 135, 147, 153, 171, 175, 207, 245, 261, 275, 297, 325, 333, 363, 369, 375, ...
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
63 is a term because sigma(63^3) = 437200 is not divisible by sigma(63) = 104.
MATHEMATICA
Select[2Range[400] - 1, Not[Divisible[DivisorSigma[1, #^3], DivisorSigma[1, #]]] &] (* Alonso del Arte, Jul 20 2016 *)
PROG
(PARI) isok(n) = sigma(n^3) % sigma(n) != 0 && n % 2 == 1
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jul 20 2016
STATUS
approved