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

Author

Pieter Post, May 08 2015

Keywords

• nonn
• base
• more

Comments

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

Examples

			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).
		

Crossrefs

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

Programs

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))

Extensions

a(14) from Giovanni Resta, May 09 2015

a(15) from Chai Wah Wu, Nov 30 2015