A132631 Numbers k such that sigma(k+1)-k-1 divides sigma(k)-k, where sigma(k) is sum of positive divisors of n.
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
Offset: 1
Examples
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
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Maple
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
Select[Range[2,200],Divisible[DivisorSigma[1,#]-#,DivisorSigma[1,#+1]-#-1]&] (* Harvey P. Dale, May 20 2017 *)
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