A227227 Numbers k such that k*sum_of_digits(k) is a perfect cube.

0, 1, 8, 81, 125, 512, 1000, 1331, 2592, 6400, 8000, 10125, 19683, 20736, 34300, 35937, 36125, 46656, 59319, 74088, 81000, 123823, 125000, 157464, 185193, 268912, 279936, 328509, 373248, 421875, 431244, 469567, 474552, 481474, 512000, 592704, 658503, 795906

Offset

1,3

Links

Derek Orr, Table of n, a(n) for n = 1..461

Example

512*(5+1+2) = 4096 = 16^3. Hence, 512 is a term of the sequence.

Mathematica

Select[Range@ 1000000, IntegerQ@ Power[# Plus @@ IntegerDigits@ #, 1/3] == True &] (* Michael De Vlieger, Mar 23 2015 *)

Prog

(Python)
def DS(n):
    return sum(int(i) for i in str(n))
def a(n):
    k = 0
    nDSn = n * DS(n)
    while k <= n:
        if k**3 == nDSn:
            return True
        if k**3 > nDSn:
            return False
        k += 1
[n for n in range(10**5) if a(n)]
# Simplified by Derek Orr, Mar 22 2015
(Sage)
n=100000 # change n for more terms
[x for x in [0..n] if floor((x*sum(Integer(x).digits(base=10)))^(1/3))==(x*sum(Integer(x).digits(base=10)))^(1/3)] # Tom Edgar, Sep 21 2013
(PARI) for(n=0, 10^6, if((n==0) || ispower(n*sumdigits(n), 3), print1(n, ", "))) \\ Derek Orr, Mar 22 2015

Crossrefs

Cf. A227224.

Sequence in context: A274855 A301939 A302417 * A303184 A302325 A303018

Adjacent sequences: A227224 A227225 A227226 * A227228 A227229 A227230

Keyword

nonn,base,easy

Author

Derek Orr, Sep 19 2013

Status

approved