cp's OEIS Frontend

A257784 Numbers n such that the sum of the digits squared times the sum of the digits of n to some power equals n.

%I A257784 #26 Mar 23 2020 06:21:11
%S A257784 0,1,512,2511,4913,5832,17576,19683,24624,32144,37000,111616,382360,
%T A257784 415000,420224,2219400,14041600,16328000,19300032,30681423,39203125,
%U A257784 62025728,78535423,186836625,214292000,432265248,1120141312,3479669440,18529084125,25342447725
%N A257784 Numbers n such that the sum of the digits squared times the sum of the digits of n to some power equals n.
%C A257784 When the power is 1 the numbers are the cubes of their digit sum (A061209).
%C A257784 There are no 2-digit and 18-digit terms. - _Chai Wah Wu_, Jan 11 2016
%H A257784 Giovanni Resta and Chai Wah Wu, <a href="/A257784/b257784.txt">Table of n, a(n) for n = 1..80</a> n = 1..43 from Giovanni Resta
%e A257784 For power 2: 24624 = (2+4+6+2+4)^2*(2^2+4^2+6^2+2^2+4^2).
%e A257784 For power 3: 111616 = (1+1+1+6+1+6)^2*(1^3+1^3+1^3+6^3+1^3+6^3).
%o A257784 (Python)
%o A257784 # WARNING: this prints numbers in the sequence, but not in increasing order.
%o A257784 def moda(n,a):
%o A257784     kk = 0
%o A257784     while n > 0:
%o A257784         kk= kk+(n%10)**a
%o A257784         n =int(n//10)
%o A257784     return kk
%o A257784 def sod(n):
%o A257784     kk = 0
%o A257784     while n > 0:
%o A257784         kk= kk+(n%10)
%o A257784         n =int(n//10)
%o A257784     return kk
%o A257784 for a in range (1, 10):
%o A257784     for c in range (1, 10**8):
%o A257784         if c==sod(c)**2*moda(c,a):
%o A257784             print(c, end=",")
%Y A257784 Cf. A061209, A115518, A130680.
%K A257784 base,nonn
%O A257784 1,3
%A A257784 _Pieter Post_, May 08 2015
%E A257784 a(16)-a(30) from _Giovanni Resta_, May 09 2015