A067075 -id:A067075 - cp's OEIS frontend

A061912 a(n) is the smallest m for which sqrt(sum of digits of m^2) = n.

0, 1, 2, 3, 13, 67, 264, 1667, 16667, 94863, 1643167, 29983327, 706399164, 31144643167, 1296109172867, 62441868958167, 6927459779738887, 447213595487659543, 77453069648658793167, 14104963594032775808167, 3146266035952345970972687

Offset: 0

Asher Auel, May 17 2001

a(15) <= 62441868958167. - Donovan Johnson, Jul 10 2012

a(21) <= 29999999949999914454883190583. a(22) <= 948566760423324122079007168333. - Zhining Yang, Jun 21 2024

			Sum of digits of 13^2 = sum of digits of 169 = 16 is the first occurrence of 4^2, so a(4) = 13.

Mathematical Reflections, Solution to Problem J307, Issue 5, 2014, p. 1.

Cf. A007953, A004159, A061909, A061910, A061911, A067072.

Cf. A067075, A286650.

f := []: a := 1: for i from 1 to 10 do for j from 1 do if sqrt(convert(convert(j^2,base,10),`+`)) = i then f := [op(f),j]; a := j; break fi; od; od; f;

t={}; m=0; Do[While[Sqrt[Total[IntegerDigits[m^2]]] != n, m++]; AppendTo[t, m], {n,0,9}]; t (* Jayanta Basu, May 06 2013 *)

a(n) = my(k=0); while(sumdigits(k^2) != n^2, k++); k; \\ Michel Marcus, Jan 07 2017

a(11) from John W. Layman, Jan 10 2002
a(12) from Ryan Propper, Jul 07 2005
a(13) from Zak Seidov, Jan 27 2011
a(14) from Donovan Johnson, Jul 10 2012
a(15)-a(20) from Zhining Yang, Jun 21 2024

A107679 Numbers n such that sum of digits of n^3 is 2^3 = 8.

Original entry on oeis.org

2, 5, 8, 11, 20, 50, 80, 101, 110, 200, 500, 800, 1001, 1010, 1100, 2000, 5000, 8000, 10001, 10010, 10100, 11000, 20000, 50000, 80000, 100001, 100010, 100100, 101000, 110000, 200000, 500000, 800000, 1000001, 1000010, 1000100, 1001000, 1010000, 1100000

Offset: 1

Zak Seidov, Jun 10 2005

Vincenzo Librandi, Table of n, a(n) for n = 1..50

Cf. A004164 (sum of digits of cubes), A067075, A159462, A159463.

[ n: n in [1..2*10^6] | 8 eq (&+Intseq(n^3)) ]; // Vincenzo Librandi, Aug 13 2017

Do[If[Total[IntegerDigits[m^3]]==8, Print[m]], {m, 2*10^7}] (* Vincenzo Librandi, Aug 13 2017 *)

isok(n) = sumdigits(n^3) == 8; \\ Michel Marcus, Aug 12 2017

More terms from Michel Marcus, Oct 09 2013

A159462 Numbers n with property that sod(n^3) = 5^3.

Original entry on oeis.org

341075, 423299, 446423, 542657, 638144, 661529, 667163, 786599, 798899, 828113, 837719, 841733, 842921, 861683, 869513, 879353, 883595, 887813, 887819, 905882, 912176, 912299, 919676, 923144, 927926, 928259, 928298, 943538, 950216, 954635

Offset: 1

Zak Seidov, Apr 12 2009

Numbers n with property that A007953(n^3) = 5^3.

			341075^3 = 39677989979796875, 3+9+6+7+7+9+8+9+9+7+9+7+9+6+8+7+5 = 125 = 5^3.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A054966 Numbers that are congruent to {0, 1, 8} mod 9. A054966 Possible sums of digits of cubes. A067075 a(n) = smallest number m such that the sum of the digits of m^3 is equal to n^3. A007953 Digital sum (i.e. sum of digits) of n. A159463 Numbers n with property that sod(n^3) = 6^3.

Select[Range[10^6],Total[IntegerDigits[#^3]]==125&] (* Harvey P. Dale, Jun 29 2022 *)

isok(n) = sumdigits(n^3) == 125; \\ Michel Marcus, Oct 16 2013

A159463 Numbers n with property that sod(n^3) = 6^3.

Original entry on oeis.org

3848163483, 4462569999, 4479677412, 4586158119, 4594661259, 4594665192, 4594700889, 4625720379, 4641588459, 5644008999, 5828410842, 5833034823, 5838252576, 5848025709, 6453471192, 6617331999, 6619097067, 6686657169, 7107126942, 7230291999, 7277907183

Offset: 1

Zak Seidov, Apr 12 2009

Numbers n with property that A007953(n^3) = 6^3.

			3848163483^3 = 56984998629886989599887999587, 5+6+9+8+4+9+9+8+6+2+9+8+8+6+9+8+9+5+9+9+8+8+7+9+9+9+5+8+7 = 216 = 6^3.

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A054966 Numbers that are congruent to {0, 1, 8} mod 9. A054966 Possible sums of digits of cubes. A067075 a(n) = smallest number m such that the sum of the digits of m^3 is equal to n^3. A007953 Digital sum (i.e., sum of digits) of n.

Numbers n such that sum of digits of n^3 is k^3: A107679 (k=2), A290842 (k=3), A290843 (k=4), A159462 (k=5), this sequence (k=6).

a(16)-a(21) from Seiichi Manyama, Aug 12 2017

A067074 a(n) = smallest cube m^3 such that the sum of the digits of m^3 is equal to n^3.

Original entry on oeis.org

0, 1, 8, 19683, 1693669888, 39677989979796875, 56984998629886989599887999587

Offset: 0

Amarnath Murthy, Jan 05 2002

If n = 6*k, a(n) <= A272066(n^3/18). - Seiichi Manyama, Aug 12 2017

			a(3) = 19683 as it is the smallest cube whose digit sum = 27 = 3^3.

Cf. A000578, A067072, A067075.

a(n) = A067075(n)^3. - R. J. Mathar, Aug 23 2018

Corrected by Stefan Steinerberger, Nov 09 2005, using existing corrections to A067075

a(0)=0 prepended by Seiichi Manyama, Aug 12 2017

A290843 Numbers k such that the sum of digits of k^3 is 4^3 = 64.

Original entry on oeis.org

1192, 1366, 1426, 1435, 1753, 1786, 1813, 1816, 1912, 1942, 1999, 2116, 2389, 2395, 2398, 2413, 2566, 2599, 2632, 2635, 2653, 2692, 2713, 2872, 2899, 2992, 3022, 3031, 3103, 3199, 3289, 3295, 3298, 3301, 3355, 3361, 3382, 3394, 3409, 3415, 3442, 3466, 3475

Offset: 1

Seiichi Manyama, Aug 12 2017

			1192^3 = 1693669888, 1 + 6 + 9 + 3 + 6 + 6 + 9 + 8 + 8 + 8 = 64 = 4^3.
11*(10^(n+2) + 1) is a term for all n > 0. - _Altug Alkan_, Aug 12 2017

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Numbers k such that sum of digits of k^3 is m^3: A107679 (m=2), A290842 (m=3), this sequence (m=4), A159462 (m=5), A159463 (m=6).

Cf. A067075.

Select[Range[3500],Total[IntegerDigits[#^3]]==64&] (* Harvey P. Dale, Aug 04 2019 *)

isok(n) = sumdigits(n^3) == 64; \\ Altug Alkan, Aug 12 2017

A286650 a(n) is the smallest number m such that the sum of the digits of m^4 is equal to n^4.

Original entry on oeis.org

0, 1, 11, 1434, 1269681358

Offset: 0

Seiichi Manyama, Aug 15 2017

			a(2) = 11 as 11^4 = 14641 is the smallest fourth power whose digit sum = 16 = 2^4.

Cf. A061912, A067075, A069648, A291145.

Cf. A000583 (n^4), A055565 (sum of digits of n^4).

{a(n) = my(k=0); while(sumdigits(k^4) != n^4, k++); k}

A290842 Numbers k such that the sum of digits of k^3 is 3^3 = 27.

Original entry on oeis.org

27, 33, 36, 39, 42, 54, 57, 69, 72, 75, 78, 84, 87, 93, 105, 108, 111, 114, 135, 138, 147, 162, 165, 168, 174, 177, 219, 222, 225, 228, 231, 234, 258, 267, 270, 273, 276, 285, 291, 294, 312, 318, 321, 330, 342, 345, 348, 351, 360, 369, 381, 384, 390, 405, 417

Offset: 1

Seiichi Manyama, Aug 12 2017

It is obvious that if k is in this sequence, then so is 10*k. Additionally, this sequence contains other infinite subsequences. For example, 10^(2*k) + 10^k + 1 is in this sequence for all k > 0. - Altug Alkan, Aug 12 2017

			27^3 = 19683, 1 + 9 + 6 + 8 + 3 = 27 = 3^3.

Seiichi Manyama, Table of n, a(n) for n = 1..500

Numbers k such that sum of digits of k^3 is m^3: A107679 (m=2), this sequence (m=3), A290843 (m=4), A159462 (m=5), A159463 (m=6).

Cf. A067075.

isok(n) = sumdigits(n^3) == 27; \\ Altug Alkan, Aug 12 2017

A328364 a(n) is the smallest number m such that the sum of the digits of m^5 is equal to n^5.

Original entry on oeis.org

0, 1, 47, 13174539

Offset: 0

Seiichi Manyama, Oct 14 2019

			a(2) = 47 as 47^5 = 229345007 is the smallest fifth power whose digit sum = 32 = 2^5.

Cf. A061912, A069648, A067075, A286650, A328374.

Cf. A000584 (n^5), A055566 (sum of digits of n^5).

{a(n) = my(k=0); while(sumdigits(k^5) != n^5, k++); k}

cp's OEIS Frontend

A061912 a(n) is the smallest m for which sqrt(sum of digits of m^2) = n.

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A107679 Numbers n such that sum of digits of n^3 is 2^3 = 8.

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A159462 Numbers n with property that sod(n^3) = 5^3.

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A159463 Numbers n with property that sod(n^3) = 6^3.

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A067074 a(n) = smallest cube m^3 such that the sum of the digits of m^3 is equal to n^3.

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A290843 Numbers k such that the sum of digits of k^3 is 4^3 = 64.

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A286650 a(n) is the smallest number m such that the sum of the digits of m^4 is equal to n^4.

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A290842 Numbers k such that the sum of digits of k^3 is 3^3 = 27.

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