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A063906
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Numbers m such that m = 2*sigma(m)/3 - 1.
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6
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OFFSET
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1,1
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COMMENTS
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Original title: numbers n such that t(n) = s(n), where s(n) = sigma(n)-n-1 and t(n) = |s(n)-n|+1.
All terms are odd and satisfy A009194(m) = 1 or 3.
Includes 3^(k-1)*(3^k-4) for k in A058959.
The first few terms of this form are 15, 207, 19359, 36472996363223648799.
Other terms include 3^15*43048567*1003302465131 = 619739816695811335405066239 and 3^15*43049011*808868950607 = 499643410492503517919703039. (End)
In other words, numbers m such that sigma(m)/(m+1) = 3/2. - Michel Marcus, Jan 03 2023
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LINKS
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EXAMPLE
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sigma(1207359) = 1811040; 1811040 - 1207359 - 1 = 603680; abs(603680 - 1207359) + 1 = 603680.
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MAPLE
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select(n -> numtheory:-sigma(n) = 3/2*(n+1), [seq(i, i=1..10^6, 2)]); # Robert Israel, Jan 12 2016
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MATHEMATICA
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Select[Range[10^6], 2 * DivisorSigma[1, #]/3 - 1 == # &] (* Giovanni Resta, Apr 14 2016 *)
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PROG
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(PARI) s(n) = sigma(n)-n-1;
t(n) = abs(s(n)-n)+1;
for(n=1, 10^8, if(t(n)==s(n), print1(n, ", ")))
(ARIBAS): for n := 1 to 4000000 do s := sigma(n) - n - 1; t := abs(s - n) + 1; if s = t then write(n, " "); end; end;
(Magma) [n: n in [1..6*10^6] | 2*DivisorSigma(1, n)/3-1 eq n]; // Vincenzo Librandi, Oct 10 2017
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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