A239055 Numbers n such that the equation Sd(n^k) = Sd(k^n) is satisfied for a k < n, where Sd(x) is the sum of the digits of x.

4, 10, 12, 15, 16, 18, 28, 39, 40, 52, 58, 63, 69, 72, 82, 87, 93, 100, 106, 120, 123, 126, 128, 138, 144, 186, 195, 212, 213, 214, 222, 225, 249, 263, 273, 274, 282, 286, 292, 294, 313, 321, 322, 339, 347, 375, 381, 386, 388, 400, 402, 426, 432, 436, 448, 454

Offset

1,1

Comments

Obviously if k=n then Sd(n^k)=Sd(k^n). The sequence lists the numbers n whose minimum k that satisfies the equation is less than n.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..100

Example

For n = 16 the minimum k is 14. In fact 16^14 = 72057594037927936 and the sum of its digits is 85 while 14^16 = 2177953337809371136 and the sum of its digits is, again, 85.

Maple

S:=proc(s) local w, j; w:=convert(s, base, 10); sum(w[j], j=1..nops(w)); end:
P:=proc(q) local k, n; for n from 1 to q do k:=0;
while S(n^k)<>S(k^n) do k:=k+1; od; if k<n then print(n); fi; od;
end: P(10^5);

Mathematica

Select[Range@ 454, AnyTrue[Range[# - 1], Function[x, Total@ IntegerDigits[#^x] == Total@ IntegerDigits[x^#]]] &] (* Michael De Vlieger, Sep 22 2015, Version 10 *)

Prog

(PARI) isok(n) = {for (k=1, n-1, if (sumdigits(n^k)==sumdigits(k^n), return (1)); ); } \\ Michel Marcus, Sep 22 2015

Crossrefs

Cf. A007953.

Sequence in context: A023693 A299634 A181053 * A295129 A287338 A077654

Adjacent sequences: A239052 A239053 A239054 * A239056 A239057 A239058

Keyword

nonn,base

Author

Paolo P. Lava, Apr 02 2014

Status

approved