A373727 -id:A373727 - cp's OEIS frontend

A380052 a(n) is the largest number whose cube is an n-digit cube which has the maximum sum of digits (A373727(n)).

2, 4, 9, 19, 46, 92, 208, 453, 942, 1966, 4289, 9949, 12599, 43795, 99829, 215083, 446423, 989353, 2131842, 4081435, 9850783, 20714797, 43967926, 92827483, 190349299, 464110759, 989554129, 2132590453, 4559677342, 9654499999, 21253161559, 31037622999, 99594689449, 181610950229

Offset: 1

Zhining Yang, Jan 11 2025

			For n=7, among cubes which are 7 digits long the maximum sum of digits is A373727(7) = 46 and this is attained by 3 cubes, the largest of which is 208^3 = 8998912 so that a(7) = 208.

Cf. A373727, A379869.

Other powers: A379298, A380797, A380566, A380193.

C
```
/* See A373727. */
```

Table[SortBy[Map[{#, Total@IntegerDigits[#^3]} &,
     Range[Ceiling@CubeRoot[10^(n - 1)], CubeRoot[10^n - 1]]],
    Last][[-1]][[1]], {n, 18}]

A379869 a(n) is the least number whose cube is an n-digit cube which has the maximum sum of digits (A373727(n)).

Original entry on oeis.org

2, 4, 9, 19, 31, 92, 157, 423, 927, 1966, 4289, 8782, 12599, 30355, 99829, 215083, 341075, 989353, 2131842, 4081435, 8334082, 20632999, 43967926, 88316866, 190349299, 364929616, 735501679, 1948602829, 3036548692, 9654499999, 17087193298, 31037622999, 99594689449, 181610950229, 426932901019, 956829383603

Offset: 1

Zhining Yang, Jan 11 2025

			For n=7, the maximum sum of digits for a 7-digit cube is A373727(7) = 46 and this is attained by 3 cubes, the smallest of which is 157^3 = 3869893 so that a(7) = 157.

Cf. A373727, A380052.

Other powers: A380111, A379650, A380567.

C
```
/* See A373727. */
```

Table[t =SortBy[Map[{#, Total@IntegerDigits[#^3]} &,
    Range[Ceiling@CubeRoot[10^(n - 1)], CubeRoot[10^n - 1]]], Last];
 Select[t, #[[2]] == t[[-1]][[2]] &][[1, 1]], {n, 18}]

a(26) and a(35) corrected by Kevin Ryde, Apr 03 2025

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

A374025 a(n) is the largest digit sum of all n-digit fifth powers.

Original entry on oeis.org

1, 5, 9, 27, 27, 36, 45, 46, 52, 63, 72, 80, 89, 90, 99, 104, 108, 119, 126, 143, 137, 152, 157, 162, 175, 180, 182, 189, 198, 208, 209, 216, 225, 234, 236, 250, 253, 270, 270, 284, 286, 288, 297, 310, 315, 323, 324, 334, 341, 346, 351, 364

Offset: 1

Zhining Yang, Jun 25 2024

			a(5) = 27 because 27 is the largest digital sum encountered among all 5-digit fifth powers (16807, 32768, 59049).

Cf. A055566, A018141, A018143, A348300, A373727, A373914.

Table[Max@Map[Total@IntegerDigits[#^5] &, Range[Ceiling[10^((n - 1)/5)], Floor[(10^n-1)^(1/5)]]], {n, 40}]

from sympy import integer_nthroot
def A374025(n): return max(sum(int(d) for d in str(m**5)) for m in range((lambda x:x[0]+(x[1]^1))(integer_nthroot(10**(n-1),5)),1+integer_nthroot(10**n-1,5)[0])) # Chai Wah Wu, Jun 26 2024

a(41)-a(49) from Chai Wah Wu, Jun 26 2024

a(50)-a(52) from Chai Wah Wu, Jun 27 2024

A373994 a(n) is the largest digit sum of all n-digit sixth powers.

Original entry on oeis.org

1, 10, 18, 19, 27, 28, 45, 37, 46, 64, 64, 81, 82, 82, 91, 100, 100, 118, 117, 126, 136, 136, 154, 154, 163, 163, 172, 181, 181, 190, 199, 208, 217, 226, 235, 235, 243, 244, 261, 262, 280, 280, 280, 289, 298, 298, 307, 325, 325, 325, 334, 352, 352, 361, 370

Offset: 1

Zhining Yang, Jun 26 2024

			a(6) = 28 because 28 is the largest digital sum encountered among all 6-digit sixth powers (117649, 262144, 531441).

Kevin Ryde, C Code

Cf. A001014, A348300, A373727, A373914, A374025.

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

Table[Max@Map[Total@IntegerDigits[#^6] &, Range[Ceiling[10^((n - 1)/6)], Floor[(10^n-1)^(1/6)]]], {n, 42}]

cp's OEIS Frontend

A380052 a(n) is the largest number whose cube is an n-digit cube which has the maximum sum of digits (A373727(n)).

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A379869 a(n) is the least number whose cube is an n-digit cube which has the maximum sum of digits (A373727(n)).

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

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A374025 a(n) is the largest digit sum of all n-digit fifth powers.

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A373994 a(n) is the largest digit sum of all n-digit sixth powers.

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