The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A350300 Irregular triangle read by rows: The n-th row lists the "n-th power friends", numbers k such that digsum(digsum(k^n)^n) = k but digsum(k^n) is not k. 2
 13, 16, 19, 28, 18, 27, 23, 29, 31, 34, 38, 44, 46, 47, 55, 56, 62, 65, 64, 73, 35, 80, 109, 127, 52, 70, 112, 118, 121, 127, 136, 181, 97, 108, 117, 130, 144, 153, 88, 144, 153, 160, 139, 152, 153, 154, 161, 173, 176, 178, 181, 184, 187, 189, 189, 198 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Two numbers x and y with x < y are said to be "n-th power friends" if digsum(x^n)=y and digsum(y^n)=x. This sequence lists both x and y; A350301 lists just the x's and A350302 lists just the y's. The name "n-th power friends" comes from "The Man Who Counted", where the n=2 case is discussed: "The digits of the number 256 add up to 13. The square of 13 is 169. The digits of 169 add up to 16. As a result, the numbers 13 and 16 have a curious relation, which we could call a quadratic friendship" (p. 33). There are finitely many such k for a particular n since digsum(digsum(k^n)^n) <= 9n log_10(9n log_10(k)). There are no such k for n=1 since either k is a single digit or else digsum(k) < k. REFERENCES M. Tahan, The Man Who Counted: A Collection of Mathematical Adventures, W. W. Norton & Company, 1993. LINKS Table of n, a(n) for n=2..57. EXAMPLE Triangle begins: 13, 16; 19, 28; 18, 27; 23, 29, 31, 34; ; 38, 44, 46, 47, 55, 56, 62, 65; 64, 73; 35, 80; ; ; 109, 127; 52, 70, 112, 118, 121, 127, 136, 181; 97, 108, 117, 130; 144, 153; 88, 144, 153, 160; ... 18 and 27 are in row n=4 since 18^4 = 104976 and 1 + 0 + 4 + 9 + 7 + 6 = 27, and 27^4 = 531441 and 5 + 3 + 1 + 4 + 4 + 1 = 18. PROG (Python 3) from math import log n = 1 while n <= 50: k = 2 while 9*n*log(9*n*log(k, 10), 10) >= k: s1 = sum(int(d) for d in str(k**n)) s2 = sum(int(d) for d in str(s1**n)) if k != s1 and k == s2: print(k) k += 1 n += 1 CROSSREFS Cf. A007953, A350301, A350302. Sequence in context: A295327 A179202 A159975 * A110623 A163674 A280062 Adjacent sequences: A350297 A350298 A350299 * A350301 A350302 A350303 KEYWORD nonn,base,tabf AUTHOR Daniel Carter, Dec 23 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 00:14 EDT 2023. Contains 365554 sequences. (Running on oeis4.)