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, 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.

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: A345405 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