A067177 -id:A067177 - cp's OEIS frontend

A004164 Sum of digits of n^3.

0, 1, 8, 9, 10, 8, 9, 10, 8, 18, 1, 8, 18, 19, 17, 18, 19, 17, 18, 28, 8, 18, 19, 17, 18, 19, 26, 27, 19, 26, 9, 28, 26, 27, 19, 26, 27, 19, 26, 27, 10, 26, 27, 28, 26, 18, 28, 17, 18, 28, 8, 18, 19, 35, 27, 28, 26, 27, 19, 26, 9, 28, 26, 18, 19, 26, 36, 19

Offset: 0

N. J. A. Sloane

For the digital root of n^3 see A073636.

The greedy inverse is 1, -1, -1, -1, -1, -1, -1, 2, 3, 4, -1, -1, -1, -1, -1, -1, 14, 9, 13, -1, -1, .. where -1 means the inverse does not exist. Essentially provided by A067177. - R. J. Mathar, Jul 19 2024

Nathaniel Johnston, Table of n, a(n) for n = 0..10000
Michael Drmota, Christian Mauduit, Joël Rivat, The sum-of-digits function of polynomial sequences, J. Lond. Math. Soc. (2) 84(2011), no. 1, 81--102. MR2819691 (2012f:11193).

Cf. A004159, A007953.

A004164 := proc(n) return add(d, d=convert(n^3,base,10)): end: seq(A004164(n),n=0..100); # Nathaniel Johnston, May 05 2011

DigitSum[Range[0, 100]^3] (* Paolo Xausa, Jul 03 2024 *)

a(n) = sumdigits(n^3); \\ Michel Marcus, Jul 07 2019

A067075 a(n) is the smallest number m such that the sum of the digits of m^3 is equal to n^3.

Original entry on oeis.org

0, 1, 2, 27, 1192, 341075, 3848163483, 2064403725539899

Offset: 0

Amarnath Murthy, Jan 05 2002

If n = 6*k, a(n) <= A002283(n^3/18). For example, a(6) = 3848163483 <= A002283(6^3/18) = 999999999999. - Seiichi Manyama, Aug 12 2017
a(n) >= ceiling(A051885(n^3)^(1/3)). For example a(7) >= ceiling(A051885(7^3)^(1/3)) = ceiling((2*10^38-1)^(1/3)) = 5848035476426 - David A. Corneth, Aug 23 2018
From Zhining Yang, Jun 20 2024: (Start)
a(8) <= 99995999799995999999999.
a(9) <= 999699989999999949999999999999999.
a(10) <= 199999999929999999999949999999999999999999999.
(End)

			a(3) = 27 as 27^3 = 19683 is the smallest cube whose digit sum = 27 = 3^3.

Cf. A051885, A061912, A067074. Subsequence of A067177.

Do[k = 1; While[Plus @@ IntegerDigits[k^3] != n^3, k++ ]; Print[k], {n, 1, 6}] (* Ryan Propper, Jul 07 2005 *)

a(n) = my(k=0); while (sumdigits(k^3) != n^3, k++); k; \\ Seiichi Manyama, Aug 12 2017

Corrected and extended by Ryan Propper, Jul 07 2005
a(0)=0 prepended by Seiichi Manyama, Aug 12 2017
a(7) from Zhining Yang, Jun 20 2024

A061096 Let k = n-th number that is a possible digit-sum for a cube (A054966); sequence gives smallest cube with digit-sum k.

Original entry on oeis.org

1, 8, 27, 64, 2744, 729, 2197, 17576, 19683, 6859, 148877, 287496, 438976, 778688, 2299968, 3869893, 43986977, 75686967, 174676879, 596947688, 796597983, 1693669888, 9649992689, 56888939736, 7598896696, 78898389569, 197747699976, 677298787768, 1778597976896

Offset: 0

Amarnath Murthy, Apr 19 2001

			a(5) = 2744, sum of digits = 17, the fifth term of A054966 (1,8,9,10,17,18...)

Amarnath Murthy, Fabricating a perfect cube with a given valid digit sum (to be published)

Cf. A054966, A067177.

a(n) = A067177(n)^3. - R. J. Mathar, Aug 23 2018

More terms from Sascha Kurz, Jan 28 2003

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A004164 Sum of digits of n^3.

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A067075 a(n) is the smallest number m such that the sum of the digits of m^3 is equal to n^3.

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A061096 Let k = n-th number that is a possible digit-sum for a cube (A054966); sequence gives smallest cube with digit-sum k.

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