A379869 -id:A379869 - 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}]

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]}]]

A380052 a(n) is the largest 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, 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}]

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}]

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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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

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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C

Mathematica

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