A133019 -id:A133019 - cp's OEIS frontend

A133029 Divisors of 1729, the 2nd taxicab number (also called the Hardy-Ramanujan number).

1, 7, 13, 19, 91, 133, 247, 1729

Offset: 1

Omar E. Pol, Oct 23 2007, Nov 07 2007

Note that 19 * 91 = 1729. For products of n-th prime and n-th prime written backwards, see A133019.

			7 * 247 = 1729 and 13 * 133 = 1729.

Index entries for sequences related to divisors of numbers

Cf. A000005, A018487. Taxicab numbers: A011541.

Divisors[1729] (* Alonso del Arte, Oct 11 2019 *)

divisors(1729) \\ Charles R Greathouse IV, Jun 21 2017

A133022 Product of n-th Fibonacci number and n-th Fibonacci number written backwards.

Original entry on oeis.org

0, 1, 1, 4, 9, 25, 64, 403, 252, 1462, 3025, 8722, 63504, 77356, 291421, 9760, 778743, 12697747, 12537568, 7584334, 38398140, 710406346, 208476181, 2168819074, 4004525952, 3905576425, 47722137553, 160019976838, 37728297243, 474332543035, 33479625520

Offset: 0

Omar E. Pol, Nov 07 2007

			403 = 13*31.

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A000045, A004091, A061205, A133019.

a:= n-> (f-> (s-> f*parse(cat(s[-i]$i=1..length(s))))(
          ""||f))(((<<0|1>, <1|1>>^n)[1, 2])):
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 06 2018

#*FromDigits[Reverse[IntegerDigits[#]]]&/@Fibonacci[Range[0,40]] (* Harvey P. Dale, Oct 12 2012 *)

a(n) = A000045(n) * A004091(n).

Corrected and extended by Harvey P. Dale, Oct 12 2012

A135625 Product of n-th Mersenne prime and n-th Mersenne prime written backwards.

Original entry on oeis.org

9, 49, 403, 91567, 15710338, 22299240301, 410215255975, 16028490260973271564, 3675428737957071376458418697257441432, 68870283995769119153444423083582483731047501259451576, 117132053040627211700855551462169332419627937481594387132326105147, 123777964225587033644972609912682600644825032245501533642224841942296666013617

Offset: 1

Omar E. Pol, Feb 20 2008

			a(3) = 403 because the 3rd Mersenne prime is 31 and 31*13 = 403.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000668, A133019, A135623.

read transforms : A000043 := proc(n) op(n,[2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937]) ; end: A000668 := proc(n) 2^A000043(n)-1 ; end: A135623 := proc(n) digrev(A000668(n)) ; end: A135625 := proc(n) A000668(n)*A135623(n) ; end: for n from 1 to 13 do printf("%d, ",A135625 (n) ) ; od: # R. J. Mathar, Feb 28 2008

# FromDigits[Reverse[IntegerDigits[#]]]&/@Select[2^Prime[Range[100]]-1, PrimeQ] (* Harvey P. Dale, Mar 26 2012 *)

a(n) = A000668(n)*A135623(n).

More terms from R. J. Mathar, Feb 28 2008

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

Omar E. Pol, Mar 09 2008

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

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

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

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

Cf. A008601.

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

a(n)=1729*n \\ Charles R Greathouse IV, Feb 21 2015

concat(0, Vec(1729*x/(1-x)^2 + O(x^40))) \\ Elmo R. Oliveira, Jun 23 2025

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)

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

Omar E. Pol, Mar 09 2008

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

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

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

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

Cf. A000420, A001022, A001029.

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

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

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)

A302092 Product of n-th Bell number and n-th Bell number written backwards.

Original entry on oeis.org

1, 1, 4, 25, 765, 1300, 61306, 682306, 1713960, 1567246464, 67208788225, 51487177320, 33511259427028, 2030336608089664, 42761083701194302, 7549007599307190895, 776831192562116876947, 3388911887796350381712, 649070202541887765091474, 43774861324581222789850945

Offset: 0

Vincenzo Librandi, Apr 01 2018

Conjecture: in this sequence only two semiprimes (4,25).

			a(4) = 765 because Bell(4) = 15 and 15*51 = 765.
s(5) = 1300 because Bell(5) = 52 and 52*25 = 1300.

Cf. A000110, A004098, A133019, A133022.

[Bell(n)*Seqint(Reverse(Intseq(Bell(n)))): n in [0..30]];

b:= proc(n) option remember; `if`(n=0, 1,
      add(b(n-j)*binomial(n-1, j-1), j=1..n))
    end:
a:= n-> b(n)*(s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||(b(n))):
seq(a(n), n=0..25);  # Alois P. Heinz, Apr 26 2018

BellB[#] FromDigits[Reverse[IntegerDigits[BellB[#]]]]&/@Range[0, 50]
# IntegerReverse[#]&/@BellB[Range[0,20]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 29 2019 *)

use ntheory ":all"; sub Bell {vecsum(map{stirling($[0],$,2)} 0..$[0])}  for (0..30) { my $b=Bell($); print "$ ",vecprod($b,scalar(reverse($b))),"\n" } # _Dana Jacobsen, Mar 04 2019

a(n) = A000110(n)*A004098(n).

A135626 Product of n-th perfect number and n-th perfect number written backwards.

Original entry on oeis.org

36, 2296, 344224, 66795904, 2123921902809088, 55917383475391234048, 113139095670780538912768, 18936964716073275231635792697644548096, 17844842231875188005737387074890396164121166838056340379818586412691750912

Offset: 1

Omar E. Pol, Feb 20 2008

			a(2)=2296 because the second perfect number is 28 and 28*82=2296.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000396, A133019, A135624.

# IntegerReverse[#]&/@PerfectNumber[Range[10]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 29 2020 *)

a(n) = A000396(n)*A135624(n).

More terms from R. J. Mathar, Jun 24 2009

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A133029 Divisors of 1729, the 2nd taxicab number (also called the Hardy-Ramanujan number).

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A133022 Product of n-th Fibonacci number and n-th Fibonacci number written backwards.

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A135625 Product of n-th Mersenne prime and n-th Mersenne prime written backwards.

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A138129 Multiples of 1729, the Hardy-Ramanujan number.

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A138130 Powers of 1729, the Hardy-Ramanujan number.

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A302092 Product of n-th Bell number and n-th Bell number written backwards.

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A135626 Product of n-th perfect number and n-th perfect number written backwards.

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