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A059269 Numbers n for which the number of divisors, tau(n), is divisible by 3. 7
4, 9, 12, 18, 20, 25, 28, 32, 36, 44, 45, 49, 50, 52, 60, 63, 68, 72, 75, 76, 84, 90, 92, 96, 98, 99, 100, 108, 116, 117, 121, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 160, 164, 169, 171, 172, 175, 180, 188, 196, 198, 200, 204, 207, 212, 220, 224, 225, 228 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

tau(n) is divisible by 3 iff at least one prime in the prime factorization of n has exponent of the form 3*m + 2. This sequence is an extension of the sequence A038109 in which the numbers has at least one prime with exponent 2 (the case of m = 0 here ) in their prime factorization.

The union of A211337 and A211338 is the complementary sequence to this one. [Douglas Latimer, Apr 12 2012]

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

Conjecture: a(n) ~ k*n where k = 1/(1 - prod(1 - (p-1)/(p^(3*k)))) = 3.743455... where p ranges over the primes and k ranges over the positive integers. - Charles R Greathouse IV, Apr 13 2012

EXAMPLE

a(7) = 28 because the number of divisors of 28 d(28) = 6

MAPLE

with(numtheory): for n from 1 to 1000 do if tau(n) mod 3 = 0 then printf(`%d, `, n) fi: od:

PROG

(PARI) is(n)=vecmax(factor(n)[, 2]%3)==2 \\ Charles R Greathouse IV, Apr 10 2012

(PARI) is(n)=numdiv(n)%3==0 \\ Charles R Greathouse IV, Sep 18 2015

CROSSREFS

Cf. A038109, A000005, A211337, A211338.

Sequence in context: A276885 A089910 A177880 * A081619 A038109 A067259

Adjacent sequences:  A059266 A059267 A059268 * A059270 A059271 A059272

KEYWORD

nonn,easy

AUTHOR

Avi Peretz (njk(AT)netvision.net.il), Jan 24 2001

EXTENSIONS

More terms from James A. Sellers, Jan 24 2001

STATUS

approved

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Last modified August 19 23:35 EDT 2017. Contains 290821 sequences.