

A211337


Numbers n for which the number of divisors, tau(n), is congruent to 1 modulo 3.


4



1, 6, 8, 10, 14, 15, 21, 22, 26, 27, 33, 34, 35, 38, 39, 46, 48, 51, 55, 57, 58, 62, 64, 65, 69, 74, 77, 80, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 112, 115, 118, 119, 120, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 162
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OFFSET

1,2


COMMENTS

Any term a(n) can be expressed as 1 term from A211484 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 10 are: 1, 2, 5, 10 [4 divisors]. 4 is congruent to 1 modulo 3. Thus 10 is a member of this sequence.


MATHEMATICA

Select[Range[162], Mod[DivisorSigma[0, #], 3] == 1 &] (* T. D. Noe, Apr 21 2012 *)


PROG

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


CROSSREFS

This is an extension of A030513 (numbers with 4 divisors). The union of A059269 and A211338 is the complementary sequence to this one. The definition of this sequence uses A000005 (the number of divisors of n).
Sequence in context: A036436 A036455 A291127 * A007422 A030513 A161918
Adjacent sequences: A211334 A211335 A211336 * A211338 A211339 A211340


KEYWORD

nonn


AUTHOR

Douglas Latimer, Apr 07 2012


STATUS

approved



