A257784 Numbers n such that the sum of the digits squared times the sum of the digits of n to some power equals n.

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

Cf. A061209, A115518, A130680.

Sequence in context: A255756 A254845 A254838 * A254020 A254894 A254013

Adjacent sequences: A257781 A257782 A257783 * A257785 A257786 A257787

Keyword

base,nonn

Author

Pieter Post, May 08 2015

Extensions

a(16)-a(30) from Giovanni Resta, May 09 2015

Status

approved