cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A133019 Product of n-th prime and n-th prime written backwards.

Original entry on oeis.org

4, 9, 25, 49, 121, 403, 1207, 1729, 736, 2668, 403, 2701, 574, 1462, 3478, 1855, 5605, 976, 5092, 1207, 2701, 7663, 3154, 8722, 7663, 10201, 31003, 75007, 98209, 35143, 91567, 17161, 100147, 129409, 140209, 22801, 117907, 58843, 127087
Offset: 1

Views

Author

Omar E. Pol, Oct 27 2007

Keywords

Comments

a(8) = 1729 is the second taxicab number, also called the Hardy-Ramanujan number (see A001235, A011541 and A133029).

Examples

			a(8) = 1729 because the 8th prime is 19 and 19 written backwards is 91 and 19*91 = 1729.

Links

Crossrefs

Cf. A001235, A004087, A011541, A061205, A067563, A067087, A133029. Prime numbers: A000040.

Programs

  • Mathematica
    #*FromDigits[Reverse[IntegerDigits[#]]] & /@ Prime[Range[1, 50]] (* G. C. Greubel, Oct 02 2017 *)
#*IntegerReverse[#]&/@Prime[Range[40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 29 2021 *)
  • PARI
    vector(60, n, prime(n)*subst(Polrev(digits(prime(n))), x, 10)) \\ Michel Marcus, Dec 17 2014

Formula

a(n) = A000040(n) * A004087(n)

A138129 Multiples of 1729, the Hardy-Ramanujan number.

Original entry on oeis.org

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

Views

Author

Omar E. Pol, Mar 09 2008

Keywords

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

Crossrefs

Cf. A001235, A011541, A133019, A133029, A138130.
Cf. A008601.

Programs

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)

Extensions

More terms from Elmo R. Oliveira, Jun 23 2025

A138130 Powers of 1729, the Hardy-Ramanujan number.

Original entry on oeis.org

1, 1729, 2989441, 5168743489, 8936757492481, 15451653704499649, 26715909255079893121, 46191807102033135206209, 79865634479415290771535361, 138087682014909037743984639169, 238753602203777726259349441123201, 412804978210331688702415183702014529
Offset: 0

Views

Author

Omar E. Pol, Mar 09 2008

Keywords

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

Crossrefs

Cf. A001235, A011541, A133019, A133029, A138129.
Cf. A000420, A001022, A001029.

Programs

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)

A262609 Divisors of 1728.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728
Offset: 1

Views

Author

Omar E. Pol, Nov 20 2015

Keywords

Comments

A000578(12) = 1728 is the cube of 12.
The number of divisors of 1728 is A000005(1728) = 28.
The sum of the divisors of 1728 is A000203(1728) = 5080.
The prime factorization of 1728 is 2^6 * 3^3.
1728 + 1 = A001235(1) = A011541(2) = 1729 is the Hardy-Ramanujan number.
Three examples related to cellular automata:
1728 is also the number of ON cells after 32 generations of the cellular automata A160239 and A253088.
1728 is also the total number of ON cells around the central ON cell after 24 generations of the cellular automata A160414 and A256530.
1728 is also the total number of ON cells around the central ON cell after 43 generations of the cellular automata A160172 and A255366.

Examples

			a(3) * a(26) = 3 * 576 = 1728.
a(4) * a(25) = 4 * 432 = 1728.
a(5) * a(24) = 6 * 288 = 1728.

Links

Crossrefs

Cf. A000005, A000203, A000578, A001235, A011541, A133029, A160172, A160239, A160414, A246030, A253088, A255366, A256530.

Programs

  • Mathematica
    Divisors[1728]
  • PARI
    divisors(1728)
  • Sage
    divisors(1728);

A027901 Divisors of 10^9 + 1.

Original entry on oeis.org

1, 7, 11, 13, 19, 77, 91, 133, 143, 209, 247, 1001, 1463, 1729, 2717, 19019, 52579, 368053, 578369, 683527, 999001, 4048583, 4784689, 6993007, 7518797, 10989011, 12987013, 52631579, 76923077, 90909091, 142857143, 1000000001
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

The prime factorization of 10^9 + 1 = 7 * 11 * 13 * 19 * 52579, so tau(1000000001) = 2^5 = 32. - Bernard Schott, Oct 18 2019

Examples

			7 * 142857143 = 1000000001.
11 * 90909091 = 1000000001.
13 * 76923077 = 1000000001.

Links

Crossrefs

Cf. A018768, A133029.

Programs

Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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