

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
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..15.


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))


CROSSREFS

Cf. A061209, A115518, A111434, A114135, A130680, A257784, A257768.
Sequence in context: A080161 A257554 A270393 * A098771 A276810 A024659
Adjacent sequences: A257784 A257785 A257786 * A257788 A257789 A257790


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



