A227224 Numbers n such that n*(sum of digits of n) is a perfect square.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 75, 81, 100, 121, 144, 147, 150, 169, 192, 196, 200, 225, 242, 288, 300, 320, 324, 363, 375, 400, 441, 484, 500, 507, 512, 529, 600, 640, 648, 700, 704, 735, 800, 832, 882, 900, 960, 961, 1014, 1083, 1088, 1200, 1250, 1452, 1458, 1521, 1681, 1815

Offset

1,3

Links

Table of n, a(n) for n=1..62.

Example

375*(3+7+5) = 5625 = 75^2. So, 375 is a member of this sequence.

Mathematica

Select[Range[0, 1815], IntegerQ@ Sqrt[# Plus @@ IntegerDigits@ #] &]  (* Michael De Vlieger, Apr 12 2015 *)

Prog

(Python)
def DS(n):
    s = 0
    for i in str(n):
        s += int(i)
    return s
for n in range(10**3):
    k = 0
    while k**2 <= n*DS(n):
        if k**2 == n*DS(n):
            print(n, end=', ')
            break
        else:
            k += 1
# Edited by Derek Orr Apr 10 2015
(Magma) [n: n in [0..1000] | IsSquare(n*(&+Intseq(n)))]; // Vincenzo Librandi, Sep 20 2013
(PARI) for(n=0, 2000, s=sumdigits(n); if(issquare(n*s), print1(n, ", "))) \\ Derek Orr, Apr 10 2015
(Sage) [x for x in [0..2000] if is_square(x*sum(Integer(x).digits(base=10)))] # Bruno Berselli, May 25 2015

Crossrefs

Cf. A007953.

Sequence in context: A138141 A228017 A346535 * A236750 A001102 A051004

Adjacent sequences: A227221 A227222 A227223 * A227225 A227226 A227227

Keyword

nonn,base,easy

Author

Derek Orr, Sep 19 2013

Extensions

More terms from Derek Orr, Apr 10 2015

Status

approved