cp's OEIS Frontend

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

%I A368245 #67 Jan 31 2024 00:14:30
%S A368245 4,25,64,125,196,216,289,343,2744,3375,4096,3518743761,
%T A368245 13537086546263552,15633814156853823
%N A368245 Numbers k such that there is a positive integer r for which k^(1/r) = digsum(k) - r.
%C A368245 Some other terms: 50714860157241037295616, 188031682201497672618081, 4817904819828488880132096, 13214788658781797667045376, 45587487211290846582931833112449, 112410921330388974282595778471993, 282429536481000000000000000000000000, 21936950640377856000000000000000000000. - _Chai Wah Wu_, Jan 30 2024
%e A368245 The terms 4, 25, 64, 196, and 289 are obtained for r = 2:
%e A368245   4^(1/2) = sqrt(4) = 2 = digsum(4) - 2;
%e A368245   25^(1/2) = sqrt(25) = 5 = digsum(25) - 2 = 7 - 2;
%e A368245   64^(1/2) = sqrt(64) = 8 = digsum(64) - 2 = 10 - 2;
%e A368245   196^(1/2) = sqrt(196) = 14 = digsum(196) - 2 = 16 - 2;
%e A368245   289^(1/2) = sqrt(289) = 17 = digsum(289) - 2 = 19 - 2.
%e A368245 The terms 125, 216, 343, 2744, 3375, and 4096 are obtained for r = 3:
%e A368245   125^(1/3) = 5 = digsum(125) - 3 = 8 - 3;
%e A368245   216^(1/3) = 6 = digsum(216) - 3 = 9 - 3;
%e A368245   343^(1/3) = 7 = digsum(343) - 3 = 10 - 7;
%e A368245   2744^(1/3) = 14 = digsum(2744) - 3 = 17 - 3;
%e A368245   3375^(1/3) = 15 = digsum(3375) - 3 = 18 - 3;
%e A368245   4096^(1/3) = 16 = digsum(4096) - 3 = 19 - 3.
%e A368245 The term 3518743761 is obtained for r = 6:
%e A368245   3518743761^(1/6) = 39 = digsum(3518743761) - 6 = 45 - 6.
%t A368245 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 *)
%t A368245 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
%Y A368245 Cf. A001597 (supersequence), A007953, A029837.
%Y A368245 Cf. A023106, A128912.
%K A368245 nonn,base,more
%O A368245 1,1
%A A368245 _Stefano Spezia_, Jan 23 2024
%E A368245 a(13)-a(14) from _Chai Wah Wu_, Jan 30 2024