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A358034
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Numbers k such that A234575(k,s) = s^2 where s = A007953(k).
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0
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1, 113, 313, 331, 512, 1271, 2065, 2137, 2173, 2705, 3291, 3931, 4066, 4913, 5832, 6535, 6553, 6571, 6607, 6625, 6643, 6661, 6715, 6733, 6751, 6805, 6823, 6841, 7715, 13479, 13686, 15289, 15577, 17576, 19449, 19683, 21898, 23969, 49789, 49897, 49969
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OFFSET
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1,2
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COMMENTS
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Numbers k such that, if the sum of digits of k is s, the quotient and remainder on division of k by s sum to s^2.
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LINKS
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EXAMPLE
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a(3) = 313 is a term because the sum of digits of 313 is 7, 313 = 44*7+5, and 44+5 = 49 = 7^2.
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MAPLE
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filter:= proc(n) local s, q, r;
s:= convert(convert(n, base, 10), `+`);
r:= n mod s;
q:= (n-r)/s;
q+r = s^2
end proc:
select(filter, [$1..10^6]);
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PROG
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(Python)
from itertools import count, islice
def A358034_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:(s:=sum(int(d) for d in str(n)))**2 == sum(divmod(n, s)), count(max(startvalue, 1)))
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CROSSREFS
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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STATUS
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approved
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