A061439 -id:A061439 - cp's OEIS frontend

A181402 Total number of positive integers below 10^n requiring 7 positive cubes in their representation as sum of cubes.

1, 10, 73, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121

Offset: 1

Martin Renner, Jan 28 2011

An unpublished result of Deshouillers-Hennecart-Landreau, combined with Lemma 3 from Bertault, Ramaré, & Zimmermann implies that a(4)-a(34) are all 121. Probably a(n) = 121 for all n > 3. - Charles R Greathouse IV, Jan 23 2014

F. Bertault, O. Ramaré, and P. Zimmermann, On sums of seven cubes, Math. Comp. 68 (1999), pp. 1303-1310.
Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A018890.

Cf. A002283, A061439, A130130, A181375, A181377, A181379, A181381, A181400, A181404.

A061439(n) + A181375(n) + A181377(n) + A181379(n) + A181381(n) + A181400(n) + a(n) + A181404(n) + A130130(n) = A002283(n).
Conjectured g.f.: x*(1+9*x+63*x^2+48*x^3)/(1-x). - Colin Barker, May 04 2012
Conjectured e.g.f.: 121*(exp(x) - 1) - 120*x - 111*x^2/2 - 8*x^3. - Stefano Spezia, May 21 2024

a(5)-a(7) from Lars Blomberg, May 04 2011

a(8)-a(34) from Charles R Greathouse IV, Jan 23 2014

A373727 a(n) is the largest number that is the digit sum of an n-digit cube.

Original entry on oeis.org

8, 10, 18, 28, 28, 44, 46, 54, 63, 73, 80, 82, 98, 100, 109, 118, 125, 136, 144, 154, 154, 163, 172, 181, 190, 190, 199, 208, 217, 226, 235, 243, 253, 260, 262, 278

Offset: 1

Zhining Yang, Jun 15 2024

			a(7) = 46 because 46 is the largest digital sum encountered among all 7-digit cubes (attained at 3 cubes: 3869893, 7880599, 8998912).

Kevin Ryde, C Code

Cf. A018005, A061439.

Other powers: A371728, A373914, A374025, A373994.

C
```
/* See links. */
```

Table[Max@
  Map[Total@IntegerDigits[#^3] &,
   Range[Ceiling@CubeRoot[10^(n - 1)], CubeRoot[10^n - 1]]], {n, 15}]

from sympy import integer_nthroot
def A373727(n): return max(sum(int(d) for d in str(m**3)) for m in range(1+integer_nthroot(10**(n-1)-1,3)[0],1+integer_nthroot(10**n-1,3)[0])) # Chai Wah Wu, Jun 26 2024

A083378 a(n) is the largest integer whose cube has n digits and first digit 1, except that a(2)=2.

Original entry on oeis.org

1, 2, 5, 12, 27, 58, 125, 271, 584, 1259, 2714, 5848, 12599, 27144, 58480, 125992, 271441, 584803, 1259921, 2714417, 5848035, 12599210, 27144176, 58480354, 125992104, 271441761, 584803547, 1259921049, 2714417616, 5848035476

Offset: 1

Werner S. Hürlimann (whurlimann(AT)bluewin.ch), Jun 05 2003

a(2)=2 because there is no integer with cube between 10 and 19.

A generalization to arbitrary powers is found in Hürlimann, 2004.

W. Hürlimann, Integer powers and Benford's law, International Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 39-46, 2004.
Index entries for sequences related to Benford's law

Cf. A061439, A083377, A083379, A083380.

Floor[Power[(10^Range[30])/5, (3)^-1]] (* Harvey P. Dale, Jul 15 2011 *)

a(n) = floor((10^n/5)^(1/3)).

Edited by Don Reble, Nov 05 2005

A114323 Largest number whose 5th power has n digits.

Original entry on oeis.org

1, 2, 3, 6, 9, 15, 25, 39, 63, 99, 158, 251, 398, 630, 999, 1584, 2511, 3981, 6309, 9999, 15848, 25118, 39810, 63095, 99999, 158489, 251188, 398107, 630957, 999999, 1584893, 2511886, 3981071, 6309573, 9999999, 15848931, 25118864, 39810717

Offset: 1

Jonathan Vos Post, Feb 06 2006

Note that the rightmost digit of n and n^5 are identical. This is to 5th powers as A061439 is to cubes and A049416 is to squares.

			a(3) = 3 because 3^5 = 243 which has 3 digits, while 4^5 = 1024 has 3 digits.
a(32) = 2511886 because 2511886^5 = 99999914106500508412371346814176 has 32 digits, while 2511887^5 = 100000113160107495177704749808207 has 33 digits.

Georg Fischer, Table of n, a(n) for n = 1..300 [First 152 terms by Vincenzo Librandi]

Cf. A061439, A049416.

[Ceiling((10^n)^(1/5))-1: n in [1..40]]; // Vincenzo Librandi, Oct 11 2011

seq(print(n, floor((10^n-1)^(1/5))), n=1..300); # Georg Fischer Apr 17 2024

Table[Floor[(10^n-1)^(1/5)],{n,40}] (* Harvey P. Dale, Dec 10 2012 *)

a(n) = sqrtnint(10^n-1, 5) /* Georg Fischer on proposal of Michel Marcus, Apr 16 2024 */

a(n) = ceiling((10^n)^(1/5)) - 1.

Data corrected by Vincenzo Librandi, Oct 11 2011

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A181402 Total number of positive integers below 10^n requiring 7 positive cubes in their representation as sum of cubes.

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A373727 a(n) is the largest number that is the digit sum of an n-digit cube.

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A083378 a(n) is the largest integer whose cube has n digits and first digit 1, except that a(2)=2.

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A114323 Largest number whose 5th power has n digits.

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