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A210732 Numbers n for which sigma*(n)=sigma*(x)+sigma*(y), where n=x+y and sigma*(n) is the sum of the anti-divisors of n. 2
6, 9, 15, 18, 21, 24, 27, 30, 31, 33, 37, 39, 43, 44, 46, 47, 53, 56, 57, 62, 65, 66, 70, 73, 74, 75, 76, 78, 81, 83, 86, 88, 90, 91, 92, 93, 97, 99, 102, 103, 106, 107, 109, 110, 114, 116, 117, 118, 119, 121, 122, 123, 125, 126, 127, 129, 131, 133, 135, 136 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

Similar to A211223 but using anti-divisors.

LINKS

Table of n, a(n) for n=3..62.

EXAMPLE

sigma*(127)=sigma*(45)+sigma*(82) that is 212=86+126.

In more than one way:

sigma*(133)=sigma*(50)+sigma*(83)=sigma*(52)+sigma*(81) that is

204=80+124=94+110.

MAPLE

with(numtheory);

A210732:=proc(q)

local a, b, c, i, j, k, n;

for n from 3 to q do

  a:=0;

  for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; fi; od;

  for i from 1 to trunc(n/2) do

   b:=0; c:=0;

   for k from 2 to i-1 do if abs((i mod k)-k/2)<1 then b:=b+k; fi; od;

   for k from 2 to n-i-1 do if abs(((n-i) mod k)-k/2)<1 then c:=c+k; fi; od;

   if a=b+c then print(n); break; fi;

  od;

od; end:

A210732(10000);

CROSSREFS

Cf. A066272, A066417, A083207, A204830, A204831, A211223-A211225.

Sequence in context: A316023 A139322 A139321 * A316024 A316025 A020648

Adjacent sequences:  A210729 A210730 A210731 * A210733 A210734 A210735

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 10 2012

STATUS

approved

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Last modified September 25 07:06 EDT 2022. Contains 356959 sequences. (Running on oeis4.)