A368245 Numbers k such that there is a positive integer r for which k^(1/r) = digsum(k) - r.

4, 25, 64, 125, 196, 216, 289, 343, 2744, 3375, 4096, 3518743761, 13537086546263552, 15633814156853823

Offset: 1

Author

Stefano Spezia, Jan 23 2024

Keywords

• nonn
• base
• more

Comments

Some other terms: 50714860157241037295616, 188031682201497672618081, 4817904819828488880132096, 13214788658781797667045376, 45587487211290846582931833112449, 112410921330388974282595778471993, 282429536481000000000000000000000000, 21936950640377856000000000000000000000. - Chai Wah Wu, Jan 30 2024

Examples

			The terms 4, 25, 64, 196, and 289 are obtained for r = 2:
  4^(1/2) = sqrt(4) = 2 = digsum(4) - 2;
  25^(1/2) = sqrt(25) = 5 = digsum(25) - 2 = 7 - 2;
  64^(1/2) = sqrt(64) = 8 = digsum(64) - 2 = 10 - 2;
  196^(1/2) = sqrt(196) = 14 = digsum(196) - 2 = 16 - 2;
  289^(1/2) = sqrt(289) = 17 = digsum(289) - 2 = 19 - 2.
The terms 125, 216, 343, 2744, 3375, and 4096 are obtained for r = 3:
  125^(1/3) = 5 = digsum(125) - 3 = 8 - 3;
  216^(1/3) = 6 = digsum(216) - 3 = 9 - 3;
  343^(1/3) = 7 = digsum(343) - 3 = 10 - 7;
  2744^(1/3) = 14 = digsum(2744) - 3 = 17 - 3;
  3375^(1/3) = 15 = digsum(3375) - 3 = 18 - 3;
  4096^(1/3) = 16 = digsum(4096) - 3 = 19 - 3.
The term 3518743761 is obtained for r = 6:
  3518743761^(1/6) = 39 = digsum(3518743761) - 6 = 45 - 6.
		

Crossrefs

Cf. A001597 (supersequence), A007953, A029837.

Cf. A023106, A128912.

Programs

Mathematica

min = 0; max = 10^8; list=Union@ Flatten@ Table[ n^expo, {expo, Prime@ Range@ PrimePi@ Log2@ max}, {n, Floor[1 + min^(1/expo)], max^(1/expo)}]; (* A001597 *)
a = {};  For[k = 1, k <=Length[list], k++, For[r = 2, r <= Ceiling[Log2[Part[list,k]]], r++, If[Part[list,k]^(1/r) == Total[IntegerDigits[Part[list,k]]]-r, AppendTo[a, Part[list,k]]]]]; a

Extensions

a(13)-a(14) from Chai Wah Wu, Jan 30 2024