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URL: https://oeis.org/A227224

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A227224
Numbers k such that k*(sum of digits of k) is a perfect square.
1
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
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
(SageMath) [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
KEYWORD
nonn,base,easy
AUTHOR
Derek Orr, Sep 19 2013
EXTENSIONS
More terms from Derek Orr, Apr 10 2015
STATUS
approved