A257786 Numbers n such that the square root of the sum of the digits times the sum of the digits of n in some power equal n.

0, 1, 27, 376, 13131, 234595324075, 54377519037479592374299, 8326623359858152426050700, 1513868951125582592290131113769528

Offset: 1

Author

Pieter Post, May 08 2015

Keywords

• base
• nonn
• more

Comments

It appears that this sequence is finite.

Examples

			376 = sqrt(3+7+6)*(3^2+7^2+6^2).
13131 = sqrt(1+3+1+3+1)*(1^7+3^7+1^7+3^7+1^7).
		

Crossrefs

Cf. A028839, A061209, A115518, A130680.

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:
        k= kk+(n%10)
        n =int(n//10)
    return kk
for a in range (1, 10):
    for c in range (1, 10**8):
        if c**2==sod(c)*moda(c,a)**2:
            print (a,c, sod(c),moda(c,a))

Extensions

a(6) from Giovanni Resta, May 09 2015

a(7)-a(9) from Chai Wah Wu, Nov 29 2015