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A257784
Numbers n such that the sum of the digits squared times the sum of the digits of n to some power equals n.
7
0, 1, 512, 2511, 4913, 5832, 17576, 19683, 24624, 32144, 37000, 111616, 382360, 415000, 420224, 2219400, 14041600, 16328000, 19300032, 30681423, 39203125, 62025728, 78535423, 186836625, 214292000, 432265248, 1120141312, 3479669440, 18529084125, 25342447725
OFFSET
1,3
COMMENTS
When the power is 1 the numbers are the cubes of their digit sum (A061209).
There are no 2-digit and 18-digit terms. - Chai Wah Wu, Jan 11 2016
LINKS
Giovanni Resta and Chai Wah Wu, Table of n, a(n) for n = 1..80 n = 1..43 from Giovanni Resta
EXAMPLE
For power 2: 24624 = (2+4+6+2+4)^2*(2^2+4^2+6^2+2^2+4^2).
For power 3: 111616 = (1+1+1+6+1+6)^2*(1^3+1^3+1^3+6^3+1^3+6^3).
PROG
(Python)
# WARNING: this prints numbers in the sequence, but not in increasing order.
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**8):
if c==sod(c)**2*moda(c, a):
print(c, end=", ")
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Pieter Post, May 08 2015
EXTENSIONS
a(16)-a(30) from Giovanni Resta, May 09 2015
STATUS
approved