A138129 Multiples of 1729, the Hardy-Ramanujan number.

0, 1729, 3458, 5187, 6916, 8645, 10374, 12103, 13832, 15561, 17290, 19019, 20748, 22477, 24206, 25935, 27664, 29393, 31122, 32851, 34580, 36309, 38038, 39767, 41496, 43225, 44954, 46683, 48412, 50141, 51870, 53599, 55328, 57057, 58786, 60515, 62244, 63973, 65702, 67431

Offset

0,2

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

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 1729*n.

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

G.f.: 1729*x/(1-x)^2.

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

a(n) = 91*A008601(n).

a(n) = 2*a(n-1) - a(n-2). (End)

Mathematica

1729Range[0, 37] (* Alonso del Arte, Feb 19 2015 *)

Prog

(PARI) a(n)=1729*n \\ Charles R Greathouse IV, Feb 21 2015
(PARI) concat(0, Vec(1729*x/(1-x)^2 + O(x^40))) \\ Elmo R. Oliveira, Jun 23 2025

Crossrefs

Cf. A001235, A011541, A133019, A133029, A138130.

Cf. A008601.

Sequence in context: A340092 A324316 A182207 * A242880 A001235 A343708

Adjacent sequences: A138126 A138127 A138128 * A138130 A138131 A138132

Keyword

easy,nonn

Author

Omar E. Pol, Mar 09 2008

Extensions

More terms from Elmo R. Oliveira, Jun 23 2025

Status

approved