A380567 -id:A380567 - 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}]

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)).

Original entry on oeis.org

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}]

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

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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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)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

C

Mathematica

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

Views

Author

Keywords

Examples

Crossrefs

Programs

C

Mathematica

Extensions