A374025 -id:A374025 - cp's OEIS frontend

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)).

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]}]]

A380566 a(n) = k is the largest k for which k^5 is n digits long and the sum of digits of k^5 is the maximum for any n digit 5th power (A374025).

Original entry on oeis.org

1, 2, 3, 6, 9, 15, 18, 37, 58, 93, 156, 179, 368, 579, 756, 1379, 2337, 3965, 6006, 9746, 14198, 25046, 38779, 60006, 98746, 151446, 231755, 389658, 585516, 819199, 1584779, 2452779, 3897999, 5400759, 9744998, 15517759, 23936959, 28737498, 62943519, 95635199, 156373159, 225142779, 351816939, 595519999

Offset: 1

Zhining Yang, Jan 26 2025

			a(14) = 579 because among all 14-digit fifth powers(399^5-630^5), 549^5=49872566977749,579^5=65071799758899, both have the maximum sum of digits, 90 = A374025(14) and 579 is the largest.

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

Cf. A374025, A379650.

Cf. A380052, A380193.

a[n_]:=Module[{m=Floor[(10^n-1)^(1/5)],max=0},For[k=m,k>=Ceiling[10^((n-1)/5)],k--,t=Total@IntegerDigits[k^5];If[t>max,s=k;max=t]];s];Table[a[n],{n,30}]

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

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

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)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A380566 a(n) = k is the largest k for which k^5 is n digits long and the sum of digits of k^5 is the maximum for any n digit 5th power (A374025).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

C

Mathematica

PARI

Python

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

C

Mathematica

Python

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

C

Mathematica