A373994 -id:A373994 - cp's OEIS frontend

A380193 a(n) is the largest number whose sixth power is an n-digit sixth power which has the maximum sum of digits (A373994(n)).

1, 2, 3, 4, 6, 7, 12, 19, 31, 46, 68, 96, 143, 206, 304, 461, 677, 977, 1194, 2136, 2896, 4633, 6373, 9763, 13817, 21542, 30643, 43693, 68123, 99812, 144083, 183967, 311296, 463976, 681017, 994333, 1441977, 2150104, 3022731, 4608562, 6765526, 9258023

Offset: 1

Zhining Yang, Jan 15 2025

			a(11) = 68 because among all 11-digit sixth powers(47^6-68^6), 64^6=68719476736 and 68^6=98867482624 have the maximum sum of digits, 96 = A373994(11) and 68 is the largest number.

Zhining Yang, Table of n, a(n) for n = 1..55 [a(47) corrected by _Kevin Ryde_, Mar 25 2025]

Cf. A373994, A380567.

Other powers: A379298, A380052, A380797, A380566.

C
```
/* See A373994. */
```

Table[t=SortBy[Map[{#,Total@IntegerDigits[#^6]}&,Range[Ceiling[10^((n-1)/6)],Floor[(10^n-1)^(1/6)]]],Last];
Select[t,#[[2]]==t[[-1]][[2]]&][[1,1]],{n,36}]

A380567 a(n) = k the least number for which k^6 is n digits long and the sum of digits of k^6 is the maximum possible for a 6th power of that length (A373994(n)).

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 12, 16, 23, 46, 64, 96, 143, 202, 277, 461, 547, 977, 1194, 2136, 2896, 3707, 5762, 9763, 13817, 16474, 25847, 43693, 51967, 72539, 121624, 172988, 271427, 463976, 681017, 751204, 1387617, 1732027, 3018897, 3515477, 6765526, 9258023

Offset: 1

Zhining Yang, Jan 26 2025

			a(11) = 64 because among all 11-digit sixth powers (47^6-68^6), 64^6=68719476736 and 68^6=98867482624 have the maximum sum of digits, 96 = A373994(11) and 64 is the least number.

Zhining Yang, Table of n, a(n) for n = 1..55

Cf. A373994, A380193.

Other powers: A379869, A380111, A379650.

C
```
/* See A373994. */
```

a[n_]:=Module[{s=Ceiling[10^((n-1)/6)],max=0},For[k=s,k<=Floor[(10^n-1)^(1/6)],k++,t=Total@IntegerDigits[k^6];If[t>max,s=k;max=t]];s];Table[a[n],{n,36}]

A373914 a(n) is the largest digit sum of all n-digit fourth powers.

Original entry on oeis.org

1, 9, 13, 19, 25, 37, 43, 52, 55, 70, 76, 79, 85, 99, 103, 108, 118, 127, 135, 142, 144, 153, 171, 166, 178, 181, 189, 198, 205, 211, 220, 232, 234, 243, 252, 261, 265, 274, 279, 283, 297, 298, 313, 316, 325, 334, 337, 346, 358

Offset: 1

Zhining Yang, Jun 22 2024

			a(3) = 13 because 13 is the largest digital sum encountered among all 3-digit fourth powers (attained at both fourth powers: 256, 625).

Kevin Ryde, C Code

Cf. A055565, A018072, A018074, A380111, A380797.

Other powers: A371728, A373727, A374025, A373994.

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

Table[Max@Map[Total@IntegerDigits[#^4] &, Range[Ceiling[10^((n - 1)/4)], Floor[(10^n-1)^(1/4)]]], {n, 32}]

a(n) = my(m=ceil(10^((n-1)/4)), M=sqrtint(sqrtint(10^n))); vecmax(apply(sumdigits, vector(M-m+1, i, (i+m-1)^4))); \\ Michel Marcus, Jun 23 2024

from sympy import integer_nthroot
def A373914(n): return max(sum(int(d) for d in str(m**4)) for m in range((lambda x:x[0]+(x[1]^1))(integer_nthroot(10**(n-1),4)),1+integer_nthroot(10**n-1,4)[0])) # Chai Wah Wu, Jun 26 2024

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

cp's OEIS Frontend

A380193 a(n) is the largest number whose sixth power is an n-digit sixth power which has the maximum sum of digits (A373994(n)).

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A380567 a(n) = k the least number for which k^6 is n digits long and the sum of digits of k^6 is the maximum possible for a 6th power of that length (A373994(n)).

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C

Mathematica

A373914 a(n) is the largest digit sum of all n-digit fourth powers.

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C

Mathematica

PARI

Python

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

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Author

Keywords

Examples

Links

Crossrefs

Programs

C

Mathematica

Python