cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

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

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

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

Crossrefs

Cf. A055567, A055572, A046459, A055575, A055576, A226971.
Cf. A152147.

Programs

  • Magma
    [n: n in [0..100] | &+Intseq(n^6) eq n ]; // Vincenzo Librandi, Feb 23 2015
  • Mathematica
    Select[Range[0,100],#==Total[IntegerDigits[#^6]]&] (* Harvey P. Dale, Oct 26 2011 *)
  • PARI
    isok(k)=sumdigits(k^6)==k \\ Patrick De Geest, Dec 13 2024
  • Sage
    [n for n in (0..70) if sum((n^6).digits()) == n] # Bruno Berselli, Feb 23 2015

A055570 Sum of digits of (a(n)^4) 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, 21, 22, 23, 24, 25, 26, 28, 36
Offset: 0

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			a(2) = 2 because 2^4 = 16 and 1+6 = 7>= 2

Crossrefs

Cf. A055565, A055575, A055568, A055569, A055571, A055572.

Programs

  • Mathematica
    Select[Range[0,50],Total[IntegerDigits[#^4]]>=#&] (* Harvey P. Dale, Jan 20 2020 *)

Extensions

Definition clarified by Harvey P. Dale, Jan 20 2020

A055571 Sum of digits of a(n)^5 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, 22, 23, 24, 25, 26, 27, 28, 31, 33, 35, 36, 37, 38, 46
Offset: 1

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			a(2) = 2 because 2^5 = 32 and 3+2 = 5>= 2

Crossrefs

Cf. A055566, A055576, A055568, A055569, A055570, A055572.

Programs

  • Mathematica
    Select[Range[0,50],Total[IntegerDigits[#^5]]>=#&] (* Harvey P. Dale, Jul 03 2021 *)

A055567 Sum of digits of n^6.

Original entry on oeis.org

0, 1, 10, 18, 19, 19, 27, 28, 19, 18, 1, 28, 45, 37, 37, 27, 37, 37, 18, 37, 10, 36, 37, 46, 36, 28, 46, 45, 37, 37, 18, 46, 37, 54, 37, 46, 45, 46, 37, 45, 19, 28, 45, 37, 46, 45, 64, 46, 36, 37, 19, 54, 55, 37, 54, 46, 55, 54, 55, 37, 27, 37, 46, 36, 64, 55, 45, 55, 64, 45
Offset: 0

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

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

Links

Crossrefs

Cf. A000012, A004159, A004164, A055565, A055566, A055572, A055577, A066588.

Programs

  • Mathematica
    DigitSum[Range[0, 100]^6] (* Paolo Xausa, Jul 03 2024 *)
  • PARI
    a(n) = sumdigits(n^6); \\ Seiichi Manyama, Nov 16 2021

A055569 Sum of digits of a(n)^3 is greater than or equal to a(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 26, 27
Offset: 0

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			a(4) = 4 because 4^3 = 64 and 6+4 = 10>= 4

Crossrefs

Cf. A004164, A046459, A055568, A055570, A055571, A055572.

Programs

  • Mathematica
    Select[Range[300],Total[IntegerDigits[#^3]]>=#&] (* Harvey P. Dale, Aug 27 2013 *)

A055568 Numbers not greater than the sum of digits of their squares.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 17
Offset: 1

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			4 is a term because 4^2 = 16 and 1+6 = 7 >= 4.

Crossrefs

Cf. A004159, A055569, A055570, A055571, A055572.

A081030 a(n) = largest k such that (sum of digits of k^n) >= k.

Original entry on oeis.org

9, 17, 27, 36, 46, 64, 68, 74, 88, 117, 123, 138, 146, 154, 199, 204, 216, 232, 232, 242, 259, 256, 284, 323, 337, 344, 341, 357, 358, 396, 443, 393, 423, 465, 477, 484, 519, 521, 533, 518, 569, 597, 591, 626, 638, 682, 666, 667, 695, 712, 698, 739, 746, 784
Offset: 1

Views

Author

David W. Wilson, Mar 02 2003

Keywords

Examples

			a(2) = 17. We have 17^2 = 289 and 2+8+9 >= 17. No number > 17 has this property.

Crossrefs

Cf. A055568, A055569, A055570, A055571, A055572.

Programs

  • Mathematica
    (* the constant 20 may need to be higher for larger n *) Table[Select[Range[20*n], Total[IntegerDigits[#^n]] >= # &][[-1]], {n, 100}] (* T. D. Noe, Oct 21 2011 *)

Extensions

Definition corrected by Harvey P. Dale, Oct 21 2011
Showing 1-7 of 7 results.

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