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A257787
Numbers n such that the sum of the digits of n to some power divided by the sum of the digits equal n.
1
1, 2, 3, 4, 5, 6, 7, 8, 9, 37, 48, 415, 231591, 3829377463694454, 56407086228259246207394322684
OFFSET
1,2
COMMENTS
The first nine terms are trivial, but then the terms become very rare. It appears that this sequence is finite.
EXAMPLE
37 = (3^3+7^3)/(3+7).
231591 = (2^7+3^7+1^7+5^7+9^7+1^7)/(2+3+1+5+9+1).
PROG
(Python)
def moda(n, a):
....kk = 0
....while n > 0:
........kk= kk+(n%10)**a
........n =int(n//10)
....return kk
def sod(n):
....kk = 0
....while n > 0:
........kk= kk+(n%10)
........n =int(n//10)
....return kk
for a in range (1, 10):
....for c in range (1, 10**6):
........if c*sod(c)==moda(c, a):
............print (a, c, moda(c, a), sod(c))
KEYWORD
nonn,base,more
AUTHOR
Pieter Post, May 08 2015
EXTENSIONS
a(14) from Giovanni Resta, May 09 2015
a(15) from Chai Wah Wu, Nov 30 2015
STATUS
approved