A055567 -id:A055567 - cp's OEIS frontend

A055565 Sum of digits of n^4.

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

A055566 Sum of digits of n^5.

Original entry on oeis.org

0, 1, 5, 9, 7, 11, 27, 22, 26, 27, 1, 14, 27, 25, 29, 36, 31, 35, 45, 37, 5, 18, 25, 29, 36, 40, 35, 36, 28, 23, 9, 34, 29, 36, 31, 35, 36, 46, 41, 36, 7, 29, 27, 31, 35, 36, 46, 32, 45, 43, 11, 27, 22, 44, 36, 37, 41, 36, 52, 47, 27, 40, 35, 45, 37, 32, 36, 25, 47, 36, 22, 35

Offset: 0

Henry Bottomley, May 26 2000

			a(2) = 5 because 2^4 = 32 and 3+2 = 5.
Trajectories under the map x->a(x):
1 ->1 ->1 ->1 ->1 ->1 ->1 ->1 ->1 ->..
2 ->5 ->11 ->14 ->29 ->23 ->29 ->23 ->29 ->..
3 ->9 ->27 ->36 ->36 ->36 ->36 ->36 ->36 ->..
4 ->7 ->22 ->25 ->40 ->7 ->22 ->25 ->40 ->..
5 ->11 ->14 ->29 ->23 ->29 ->23 ->29 ->23 ->..
6 ->27 ->36 ->36 ->36 ->36 ->36 ->36 ->36 ->..
7 ->22 ->25 ->40 ->7 ->22 ->25 ->40 ->7 ->..

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

Cf. A000012, A004159, A004164, A055565, A055567, A055571, A055576, A066588.

read("transforms") :
A055566 := proc(n)
        digsum(n^5) ;
end proc: # R. J. Mathar, Jul 08 2012

Table[Total[IntegerDigits[n^5]],{n,0,80}] (* Harvey P. Dale, Feb 12 2023 *)

a(n) = sumdigits(n^5); \\ Seiichi Manyama, Nov 16 2021

A055577 Numbers k such that the sum of digits of k^6 is equal to k.

Original entry on oeis.org

0, 1, 18, 45, 54, 64

Offset: 1

Henry Bottomley, May 26 2000

			a(2) = 18 because 18^6 = 34012224 and 3+4+0+1+2+2+2+4 = 18

Cf. A055567, A055572, A046459, A055575, A055576, A226971.

Cf. A152147.

[n: n in [0..100] | &+Intseq(n^6) eq n ]; // Vincenzo Librandi, Feb 23 2015

Select[Range[0,100],#==Total[IntegerDigits[#^6]]&] (* Harvey P. Dale, Oct 26 2011 *)

isok(k)=sumdigits(k^6)==k \\ Patrick De Geest, Dec 13 2024

[n for n in (0..70) if sum((n^6).digits()) == n] # Bruno Berselli, Feb 23 2015

A055572 Sum of digits of a(n)^6 is greater than or equal to a(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 39, 42, 44, 45, 46, 51, 52, 54, 64

Offset: 0

Henry Bottomley, May 26 2000

			a(2) = 2 because 2^6 = 64 and 6+4 = 10>= 2

Cf. A055567, A055577, A055568, A055569, A055570, A055571.

A336225 Table read by antidiagonals: T(n, k) = digitsum(n*k) with n >= 0 and k >= 0.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 4, 3, 0, 0, 4, 6, 6, 4, 0, 0, 5, 8, 9, 8, 5, 0, 0, 6, 1, 3, 3, 1, 6, 0, 0, 7, 3, 6, 7, 6, 3, 7, 0, 0, 8, 5, 9, 2, 2, 9, 5, 8, 0, 0, 9, 7, 3, 6, 7, 6, 3, 7, 9, 0, 0, 1, 9, 6, 10, 3, 3, 10, 6, 9, 1, 0, 0, 2, 2, 9, 5, 8, 9, 8, 5, 9, 2, 2, 0

Offset: 0

Stefano Spezia, Jul 12 2020

			The table T(n, k) begins
0   0   0   0   0   0   0   0 ...
0   1   2   3   4   5   6   7 ...
0   2   4   6   8   1   3   5 ...
0   3   6   9   3   6   9   3 ...
0   4   8   3   7   2   6  10 ...
0   5   1   6   2   7   3   8 ...
0   6   3   9   6   3   9   6 ...
0   7   5   3  10   8   6  13 ...
...

Index entries for sequences related to sum of digits.

Cf. A003991, A004092, A004159 (diagonal), A004164 (digitsum of n^3), A004247, A007953, A055565 (digitsum of n^4), A055566 (digitsum of n^5), A055567 (digitsum of n^6).

T[n_,k_]:=Total[IntegerDigits[n*k]]; Table[T[n-k,k],{n,0,12},{k,0,n}]//Flatten

PARI
```
T(n, k) = sumdigits(n*k);
```

T(n, k) = A007953(A004247(n, k)).
T(n, 1) = T(1, n) = A007953(n).
T(n, 2) = T(2, n) = A004092(n).
T(n, k) = A007953(A003991(n, k)) for n*k > 0. - Michel Marcus, Jul 13 2020.

cp's OEIS Frontend

A055565 Sum of digits of n^4.

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Maple

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Sage

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A055566 Sum of digits of n^5.

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Maple

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A055577 Numbers k such that the sum of digits of k^6 is equal to k.

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Magma

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Sage

A055572 Sum of digits of a(n)^6 is greater than or equal to a(n).

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A336225 Table read by antidiagonals: T(n, k) = digitsum(n*k) with n >= 0 and k >= 0.

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