

A211338


Numbers n for which the number of divisors, tau(n), is congruent to 2 modulo 3.


3



2, 3, 5, 7, 11, 13, 16, 17, 19, 23, 24, 29, 30, 31, 37, 40, 41, 42, 43, 47, 53, 54, 56, 59, 61, 66, 67, 70, 71, 73, 78, 79, 81, 83, 88, 89, 97, 101, 102, 103, 104, 105, 107, 109, 110, 113, 114, 127, 128, 130, 131, 135, 136, 137, 138, 139, 149, 151, 152, 154
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OFFSET

1,1


COMMENTS

The product of any 2 terms a(i)*a(j) is not a member of the sequence.
Any term a(n) can be expressed as 1 term (required to be greater than 1) from A211485 times 1 nonzero term from A000578. [Douglas Latimer, Apr 20 2012]


LINKS

Douglas Latimer, Table of n, a(n) for n = 1..1000


FORMULA

Conjecture: a(n) ~ k*n where k = 2/prod(1  (p1)/(p^(3*k))) = 2.7290077... where p ranges over the primes and k ranges over the positive integers.  Charles R Greathouse IV, Apr 13 2012


EXAMPLE

The divisors of 16 are: 1, 2, 4, 8, 16 [5 divisors]. 5 is congruent to 2 modulo 3. Thus 16 is a member of this sequence.


MATHEMATICA

Select[Range[154], Mod[DivisorSigma[0, #], 3] == 2 &] (* T. D. Noe, Apr 21 2012 *)


PROG

(PARI) {plnt=1 ; mxind=100 ; for(k=1, 10^6,
if(numdiv(k) % 3 == 2, print(k); plnt++; if(mxind+1 == plnt, break() )))}


CROSSREFS

This is an extension of A000040 (the prime numbers, which each have 2 divisors). The union of A059269 and A211337 is the complementary sequence to this one. The definition of this sequence uses A000005 (the number of divisors of n).
Sequence in context: A086070 A117093 A062063 * A167175 A026478 A211485
Adjacent sequences: A211335 A211336 A211337 * A211339 A211340 A211341


KEYWORD

nonn


AUTHOR

Douglas Latimer, Apr 07 2012


STATUS

approved



