A072083 -id:A072083 - cp's OEIS frontend

A072408 Least number > 1 which equals n-th power of the sum of its digits in decimal base.

2, 81, 512, 2401, 17210368, 34012224, 612220032, 20047612231936, 3904305912313344, 13744803133596058624, 8007313507497959524352, 2518170116818978404827136, 81920000000000000, 2670419511272061205254504361, 2759031540715333904109053133443

Offset: 1

Labos Elemer, Jun 17 2002

			a(1) = 2 > 1;
a(9) = 3904305912313344 = 54^9 = (3+9+0+4+3+0+5+9+1+2+3+1+3+3+4+4)^9.

Michael De Vlieger, Table of n, a(n) for n = 1..274
Leo Moser, Digits of Powers, Recreational Mathematics, Curiosa 145. Scripta Mathematica Vol. XIII, March-June 1947, Nos. 1-2, page 117.

Cf. A007953, A046017, A072081-A072083.

Array[Block[{k = 2}, While[k^# != Total[IntegerDigits[k^#]]^#, k++]; k^#] &, 13] (* Michael De Vlieger, Nov 05 2020 *)

a(n) = Min{ x; x=SumDigit(x)^n} = Min{x; x=A007953(x)^n}

a(n) = A046017(n)^n. - Michael De Vlieger, Nov 05 2020

A072082 Numbers divisible by the cube of the sum of their digits in base 10.

Original entry on oeis.org

1, 10, 100, 200, 500, 512, 1000, 2000, 2401, 4913, 5000, 5103, 5120, 5832, 10000, 10206, 11000, 11200, 11664, 13122, 14000, 17576, 19000, 19683, 20000, 20412, 21141, 23000, 23328, 24010, 28000, 29160, 32000, 37000, 39366, 40000, 40824

Offset: 1

Labos Elemer, Jun 14 2002

If k is a term, then 10 * k is a term. There are an infinite number of terms that are not divisible by 10. The numbers m = 24 * 10^(294 * k - 292) +1 are divisible by 7^3 = digsum(m)^3. Also, the numbers s = 491 * 10^(4624 * k - 4623) + 3, k >= 1, are divisible by 17^3 = digsum(s)^3. - Marius A. Burtea, Mar 18 2020

			k=98415: sumdigits(98415)=27, q=98415=5*27*27*27.

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A055012, A005349, A003634, A072081, A072083.

[k:k in [1..41000]| k mod &+Intseq(k)^3 eq 0]; // Marius A. Burtea, Mar 18 2020

sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]^3; If[IntegerQ[n/s], Print[n]], {n, 1, 10000}]
Select[Range[50000],Divisible[#,Total[IntegerDigits[#]]^3]&] (* Harvey P. Dale, Mar 22 2016 *)

is(n)=n%sumdigits(n)^3==0 \\ Charles R Greathouse IV, Mar 19 2020

cp's OEIS Frontend

A072408 Least number > 1 which equals n-th power of the sum of its digits in decimal base.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula