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A300796
Numbers x whose 10's complements y have the same sum of divisors of x, with x <> y.
0
3762, 4125, 4865, 5135, 5875, 6238, 37620, 41250, 42825, 44571, 48650, 48839, 49496, 50504, 51161, 51350, 55429, 57175, 58750, 62380, 376200, 389232, 397584, 399441, 412500, 417864, 428250, 434355, 436185, 445710, 446369, 472535, 481325, 483662, 483792, 486500
OFFSET
1,1
COMMENTS
Many patterns can be found, e.g. 3762*10^j, 4125*10^j, 4865*10^j, 5135*10^j, 5875*10^j, 6238*10^j, etc.
EXAMPLE
3762 is in the sequence because sigma(3762) = sigma(10^4-3762) = 9360.
5875 is in the sequence because sigma(5875) = sigma(10^4-5875) = 7488.
MAPLE
with(numtheory): P:=proc(q) local a, n;
for n from 1 to q do a:=10^(ilog10(n)+1)-n;
if n<>a and sigma(n)=sigma(a) then print(n); fi; od; end: P(10^6);
MATHEMATICA
c10Q[n_]:=Module[{c=10^IntegerLength[n]-n}, c!=n&&DivisorSigma[1, n] == DivisorSigma[1, c]]; Select[Range[500000], c10Q] (* Harvey P. Dale, Sep 24 2021 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Paolo P. Lava, Mar 13 2018
STATUS
approved