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A132631
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Numbers k such that sigma(k+1)-k-1 divides sigma(k)-k, where sigma(k) is sum of positive divisors of n.
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2
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2, 4, 6, 10, 12, 16, 18, 20, 22, 24, 28, 30, 36, 40, 42, 46, 52, 58, 60, 66, 70, 72, 78, 82, 88, 94, 96, 100, 102, 106, 108, 112, 120, 126, 130, 136, 138, 148, 150, 156, 162, 166, 172, 178, 180, 190, 192, 196, 198
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OFFSET
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1,1
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COMMENTS
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Only even numbers.
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LINKS
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EXAMPLE
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k=94 -> sigma(k)-k=1+2+47=50 sigma(k+1)-k-1=1+5+19=25 -> 50/25=2
k=120 -> sigma(k)-k=1+2+3+4+5+6+8+10+12+15+20+24+30+40+60=240 sigma(k+1)-k-1=1+11=12 -> 240/12=20
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MAPLE
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with(numtheory): P:=proc(k) if frac((sigma(k)-k)/(sigma(k+1)-k-1))=0 then k; fi; end: seq(P(n), n=2..200);
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MATHEMATICA
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Select[Range[2, 200], Divisible[DivisorSigma[1, #]-#, DivisorSigma[1, #+1]-#-1]&] (* Harvey P. Dale, May 20 2017 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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