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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 15 10:49 EDT 2021. Contains 342977 sequences. (Running on oeis4.)