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A175755 Numbers with 49 divisors. 5
46656, 1000000, 7529536, 11390625, 85766121, 113379904, 308915776, 1291467969, 1544804416, 1838265625, 3010936384, 3518743761, 9474296896, 17596287801, 27680640625, 34296447249, 38068692544, 56800235584, 75418890625, 107918163081, 164206490176, 208422380089 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers of the forms p^48 and p^6*q^6, where p and q are distinct primes.
LINKS
FORMULA
A000005(a(n)) = 49.
Sum_{n>=1} 1/a(n) = (P(6)^2 - P(12))/2 + P(48) = 0.0000226806..., where P is the prime zeta function. - Amiram Eldar, Jul 03 2022
EXAMPLE
a(1) = A114334(49); a(2) = A159765(49).
MATHEMATICA
Select[Range[100000000], DivisorSigma[0, #]==48&] (* Vladimir Joseph Stephan Orlovsky, May 06 2011 *)
PROG
(Haskell)
a175755 n = a175755_list !! (n-1)
a175755_list = m (map (^ 48) a000040_list) (map (^ 6) a006881_list) where
m xs'@(x:xs) ys'@(y:ys) | x < y = x : m xs ys'
| otherwise = y : m xs' ys
-- Reinhard Zumkeller, Nov 29 2011
(PARI) is(n)=numdiv(n)==49 \\ Charles R Greathouse IV, Jun 19 2016
CROSSREFS
Sequence in context: A057068 A223510 A251190 * A223562 A016866 A016914
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Aug 27 2010
EXTENSIONS
Extended by T. D. Noe, May 08 2011
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)