The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A257814 Numbers n such that k times the sum of the digits (d) to the power k equal n, so n=k*sum(d^k), for some positive integer k, where k is smaller than sum(d^k). 2
 2, 3, 4, 5, 6, 7, 8, 9, 50, 298, 130004, 484950, 3242940, 4264064, 5560625, 36550290, 47746195, 111971979, 129833998, 9865843497, 46793077740, 767609367921, 4432743262896, 42744572298532, 77186414790914, 99320211963544, 99335229415136, 456385296642870 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The first nine terms are trivial, but then the terms become scarce.  The exponent k must be less than the "sum of the digits" raised to the k-th power, otherwise there will be infinitely many terms containing 1's and 0's, like 11000= 5500*(1^5500+1^5500+0^5500+0^5500+0^5500). It appears this sequence is finite, because there is a resemblance with the Armstrong numbers (A005188). LINKS Chai Wah Wu, Table of n, a(n) for n = 1..54 (terms < 10^32, n = 1..53 from Giovanni Resta) EXAMPLE 50 = 2*(5^2+0^2); 484950 = 5*(4^5+8^5+4^5+9^5+5^5+0^5). PROG (Python) def mod(n, a): ....kk = 0 ....while n > 0: ........kk= kk+(n%10)**a ........n =int(n//10) ....return kk for a in range (1, 10): ....for c in range (1, 10**7): ........if c==a*mod(c, a) and a n, return (0))); k < sdk(d, k); } \\ Michel Marcus, May 30 2015 CROSSREFS Cf. A005188, A023052, A257768. Sequence in context: A219326 A252781 A024660 * A327455 A327735 A133287 Adjacent sequences:  A257811 A257812 A257813 * A257815 A257816 A257817 KEYWORD nonn,base AUTHOR Pieter Post, May 10 2015 EXTENSIONS a(16)-a(28) from Giovanni Resta, May 10 2015 STATUS approved

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

Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)