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A132631 Numbers n such that sigma(n+1)-n-1 divides sigma(n)-n, where sigma(n) is sum of positive divisors of n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Only even numbers.

LINKS

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

EXAMPLE

n=94 -> sigma(n)-n=1+2+47=50 sigma(n+1)-n-1=1+5+19=25 -> 50/25=2

n=120 -> sigma(n)-n=1+2+3+4+5+6+8+10+12+15+20+24+30+40+60=240 sigma(n+1)-n-1=1+11=12 -> 240/12=20

MAPLE

with(numtheory); P:=proc(n) local a, i; for i from 1 by 1 to n do if sigma(i)-i>0 then a:=(sigma(i)-i)/(sigma(i+1)-i-1); if a>0 and trunc(a)=a then print(i); fi; fi; od; end: P(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: A087136 A015921 A232964 * 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

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Last modified July 23 00:43 EDT 2019. Contains 325228 sequences. (Running on oeis4.)