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Numbers n such that the sum of the digits of n to some power divided by the sum of the digits equal n.
1

%I #17 Dec 02 2015 11:57:38

%S 1,2,3,4,5,6,7,8,9,37,48,415,231591,3829377463694454,

%T 56407086228259246207394322684

%N Numbers n such that the sum of the digits of n to some power divided by the sum of the digits equal n.

%C The first nine terms are trivial, but then the terms become very rare. It appears that this sequence is finite.

%e 37 = (3^3+7^3)/(3+7).

%e 231591 = (2^7+3^7+1^7+5^7+9^7+1^7)/(2+3+1+5+9+1).

%o (Python)

%o def moda(n,a):

%o ....kk = 0

%o ....while n > 0:

%o ........kk= kk+(n%10)**a

%o ........n =int(n//10)

%o ....return kk

%o def sod(n):

%o ....kk = 0

%o ....while n > 0:

%o ........kk= kk+(n%10)

%o ........n =int(n//10)

%o ....return kk

%o for a in range (1, 10):

%o ....for c in range (1, 10**6):

%o ........if c*sod(c)==moda(c, a):

%o ............print (a,c, moda(c,a),sod(c))

%Y Cf. A061209, A115518, A111434, A114135, A130680, A257784, A257768.

%K nonn,base,more

%O 1,2

%A _Pieter Post_, May 08 2015

%E a(14) from _Giovanni Resta_, May 09 2015

%E a(15) from _Chai Wah Wu_, Nov 30 2015