A138130 Powers of 1729, the Hardy-Ramanujan number.

1, 1729, 2989441, 5168743489, 8936757492481, 15451653704499649, 26715909255079893121, 46191807102033135206209, 79865634479415290771535361, 138087682014909037743984639169, 238753602203777726259349441123201, 412804978210331688702415183702014529

Offset: 0

Author

Omar E. Pol, Mar 09 2008

Keywords

• nonn
• easy

Comments

About 1729: "No," said Ramanujan, "It is a very interesting number..."

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1997, p. 153.

Links

• Wikipedia, 1729 (number).
• Index entries for linear recurrences with constant coefficients, signature (1729).

Crossrefs

Cf. A001235, A011541, A133019, A133029, A138129.

Cf. A000420, A001022, A001029.

Programs

Mathematica

1729^Range[0, 9] (* Alonso del Arte, Oct 18 2014 *)

PARI

a(n)=1729^n \\ Charles R Greathouse IV, Jan 20 2014

Formula

a(n) = 1729^n.

From Chai Wah Wu, Jan 19 2021: (Start)

a(n) = 1729*a(n-1) for n > 0.

G.f.: 1/(1 - 1729*x). (End)

From Elmo R. Oliveira, Jun 23 2025: (Start)

E.g.f.: exp(1729*x).

a(n) = A000420(n)*A001022(n)*A001029(n). (End)