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

1,1

Comments

Only even numbers.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

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

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);

Mathematica

Select[Range[2, 200], Divisible[DivisorSigma[1, #]-#, DivisorSigma[1, #+1]-#-1]&] (* Harvey P. Dale, May 20 2017 *)

Crossrefs

Cf. A132585, A132586, A132630.

Sequence in context: A015921 A232964 A348442 * A248614 A105965 A229489

Adjacent sequences: A132628 A132629 A132630 * A132632 A132633 A132634

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Aug 27 2007

Status

approved