A373914 -id:A373914 - cp's OEIS frontend

A380111 a(n) is the least number whose fourth power is an n-digit fourth power which has the maximum sum of digits (A373914(n)).

1, 3, 4, 8, 16, 26, 47, 74, 118, 308, 518, 659, 1768, 2868, 5396, 8256, 14482, 28871, 55368, 97063, 147768, 228558, 562341, 835718, 1727156, 2878406, 5458722, 8175708, 16234882, 27831542, 53129506, 98665756, 166025442, 315265896, 510466356, 904245732, 1188893858, 2298249374, 5106312756

Offset: 1

Zhining Yang, Jan 12 2025

			a(7) = 47 because among all 7-digit fourth powers, 47^4=487968 is the least one (another larger is 56^4=9834496) which has the maximum sum of digits, 43 = A373914(7).

Zhining Yang, Table of n, a(n) for n = 1..49 [a(42) and a(49) corrected by _Kevin Ryde_, Mar 29 2025]

Cf. A373914, A380797.

Other powers: A379869, A379650, A380567.

C
```
/* See A373914. */
```

Table[t=SortBy[Map[{#,Total@IntegerDigits[#^4]}&,Range[Ceiling[10^((n-1)/4)],Floor[(10^n-1)^(1/4)]]],Last];
Select[t,#[[2]]==t[[-1]][[2]]&][[1,1]],{n,24}]

A380797 a(n) is the largest number whose fourth power is an n-digit which has the maximum sum of digits (A373914(n)).

Original entry on oeis.org

1, 3, 5, 8, 16, 26, 56, 88, 118, 308, 518, 974, 1768, 2868, 5396, 8979, 17306, 28871, 55368, 97063, 167622, 289146, 562341, 835718, 1727156, 3154276, 5623116, 9397404, 17728256, 27831542, 53129506, 98665756, 166025442, 315265896, 510466356, 904245732, 1188893858, 2298249374, 5315776056

Offset: 1

Zhining Yang, Feb 03 2025

			a(7) = 56 because among all 7-digit fourth powers, 56^4=9834496 is the largest one (another smaller is 47^4=487968) which has the maximum sum of digits, 43 = A373914(7).

Cf. A373914, A380111.

Other powers: A379298, A380052, A380566, A380193.

C
```
/* See A373914. */
```

a[n_]:=Module[{m=Floor[(10^n-1)^(1/4)], max=0},
For[k=m, k>=Ceiling[10^((n-1)/4)], k--, t=Total@IntegerDigits[k^4];
If[t>max, s=k; max=t]]; s];
Table[a[n], {n, 30}]

A055565 Sum of digits of n^4.

Original entry on oeis.org

0, 1, 7, 9, 13, 13, 18, 7, 19, 18, 1, 16, 18, 22, 22, 18, 25, 19, 27, 10, 7, 27, 22, 31, 27, 25, 37, 18, 28, 25, 9, 22, 31, 27, 25, 19, 36, 28, 25, 18, 13, 31, 27, 25, 37, 18, 37, 43, 27, 31, 13, 27, 25, 37, 27, 28, 43, 18, 31, 22, 18, 34, 37, 36, 37, 34, 45, 13, 31, 27, 7

Offset: 0

Henry Bottomley, Jun 19 2000

			a(2) = 7 because 2^4 = 16 and 1+6 = 7.

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A000583, A007953, A055570, A055575 (fixed points), A373914.

Other powers: A004159, A004164, A055566, A055567, A066588.

for i from 0 to 200 do printf(`%d,`,add(j, j=convert(i^4, base, 10))) od;

a[n_Integer]:=Apply[Plus, IntegerDigits[n^4]]; Table[a[n], {n, 0, 100}] (* Vincenzo Librandi, Feb 23 2015 *)

a(n) = sumdigits(n^4); \\ Seiichi Manyama, Nov 16 2021

[sum((n^4).digits()) for n in (0..70)] # Bruno Berselli, Feb 23 2015

a(n) = A007953(A000583(n)). - Michel Marcus, Feb 23 2015

More terms from James Sellers, Jul 04 2000

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

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}]

A379650 a(n) is the least number whose fifth power is an n-digit fifth power which has the maximum sum of digits (A374025(n)).

Original entry on oeis.org

1, 2, 3, 6, 9, 15, 18, 37, 58, 93, 156, 179, 368, 549, 756, 1379, 2139, 3965, 4956, 9746, 11156, 25046, 38779, 60006, 98746, 151446, 231755, 389658, 585516, 819199, 1584779, 1776339, 3803469, 5400759, 9744998, 11463799, 23936959, 28737498, 62943519, 95635199, 156373159, 225142779, 351816939, 595519999

Offset: 1

Zhining Yang, Jan 12 2025

			a(7) = 18 because among all 7-digit fifth powers (16^5 to 25^5), 18^5=1889568 is the item which has the maximum sum of digits, 45 = A374025(7).

Zhining Yang, Table of n, a(n) for n = 1..52

Cf. A000584, A374025.

Cf. A370522, A373914, A379869, A380111.

a[n_]:=Module[{s=Floor[(10^n-1)^(1/5)],max=0},
For[k=s,k>=Ceiling[10^((n-1)/5)],k--,t=DigitSum[k^5];
If[t>max,s=k;max=t]];s];
For[n=1,n<=30,n++,Print[{n,a[n]}]]

cp's OEIS Frontend

A380111 a(n) is the least number whose fourth power is an n-digit fourth power which has the maximum sum of digits (A373914(n)).

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A380797 a(n) is the largest number whose fourth power is an n-digit which has the maximum sum of digits (A373914(n)).

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C

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A055565 Sum of digits of n^4.

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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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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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C

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A379650 a(n) is the least number whose fifth power is an n-digit fifth power which has the maximum sum of digits (A374025(n)).

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Mathematica