OFFSET
1,2
COMMENTS
A number k is in the sequence iff in its prime factorization, all primes p == 1 (mod 3) occur to such a power p^e that e != 2 (mod 3), and all primes == 2 (mod 3) occur to even powers. (3 can occur to any power.) This sequence is similar but not identical to many others; in particular, 343 is in this sequence, but not in A034022. (And here we don't have 196, although it is in A034022). - First sentence corrected and additional notes added by Antti Karttunen, Jul 03 2024, see also Robert Israel's Nov 09 2016 comment in A087943.
The asymptotic density of this sequence is 0 (Dressler, 1975). - Amiram Eldar, Jul 23 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Tewodros Amdeberhan, Victor H. Moll, Vaishavi Sharma, and Diego Villamizar, Arithmetic properties of the sum of divisors, arXiv:2007.03088 [math.NT], 2020. See p. 15 ff. [Note: the "if and only if" condition given in the beginning of Theorem 7.1 is for A003136, not for this sequence. - Antti Karttunen, Jul 04 2024]
Robert E. Dressler, A property of the phi and sigma_j functions, Compositio Mathematica, Vol. 31, No. 2 (1975), pp. 115-118.
MAPLE
select(t -> numtheory:-sigma(t) mod 3 <> 0, [$1..200]); # Robert Israel, Jan 01 2020
MATHEMATICA
Select[Range[200], !Divisible[DivisorSigma[1, #], 3] &] (* Amiram Eldar, Nov 25 2019 *)
PROG
(PARI) isok(k) = (sigma(k) % 3) != 0; \\ Michel Marcus, Nov 26 2019
(PARI) isA329963 = A353815; \\ Antti Karttunen, Jul 03 2024
(Magma) [k:k in [1..200]| DivisorSigma(1, k) mod 3 ne 0]; // Marius A. Burtea, Jan 02 2020
KEYWORD
nonn
AUTHOR
John L. Drost, Nov 25 2019
EXTENSIONS
More terms from Joshua Oliver, Nov 26 2019
Data section further extended up to a(71), to better differentiate from nearby sequences - Antti Karttunen, Jul 04 2024
STATUS
approved