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A339999
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Squares that are divisible by both the sum of their digits and the product of their nonzero digits.
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0
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1, 4, 9, 36, 100, 144, 400, 900, 1296, 2304, 2916, 3600, 10000, 11664, 12100, 14400, 22500, 32400, 40000, 41616, 82944, 90000, 121104, 122500, 129600, 152100, 176400, 186624, 202500, 219024, 230400, 260100, 291600, 360000, 419904, 435600, 504100
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OFFSET
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1,2
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LINKS
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EXAMPLE
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For the perfect square 144 = 12^2, the sum of its digits is 9, which divides 144, and the product of its nonzero digits is 16, which also divides 144 so 144 is a term of the sequence.
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MATHEMATICA
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Select[Range[720]^2, And @@ Divisible[#, {Plus @@ (d = IntegerDigits[#]), Times @@ Select[d, #1 > 0 &]}] &] (* Amiram Eldar, Jul 23 2021 *)
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PROG
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(Python)
from math import prod
def sumd(n): return sum(map(int, str(n)))
def nzpd(n): return prod([int(d) for d in str(n) if d != '0'])
def ok(sqr): return sqr > 0 and sqr%sumd(sqr) == 0 and sqr%nzpd(sqr) == 0
print(list(filter(ok, (i*i for i in range(1001)))))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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