login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A227977 Numbers n for which n = sigma*(x) = sigma*(y), where n = x + y and sigma*(n) is the sum of the anti-divisors of n. 0
154, 3136, 5536, 20066, 136036, 9550080, 78011830 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Up to a(7) the triples (n, x, y) are (154, 77, 77), (3136, 1568, 1568)(5536, 2768, 2768), (20066, 10368, 9698), (136036, 80753, 55283), (9550080, 4775040, 4775040), (78011830, 39348342, 38663488). - Giovanni Resta, Oct 08 2013

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

n = 20066 = 9698 + 10368.

Anti-divisors of 9698 are 3, 4, 5, 7, 9, 15, 17, 45, 52, 119, 163, 431, 1141, 1293, 1492, 2155, 2771, 3879, 6465 and their sum is 20066 that is equal to n.

Anti-divisors of 10368 are 5, 11, 13, 29, 55, 65, 89, 143, 145, 233, 256, 319, 377, 715, 768, 1595, 1885, 2304, 4147, 6912 and their sum is 20066 that is equal to n.

MAPLE

with(numtheory); P:=proc(q) local a, b, i, j, k, n;

for n from 1 to q do for i from 1 to trunc(n/2) do

k:=0; j:=i; while j mod 2<>1 do k:=k+1; j:=j/2; od;

a:=sigma(2*i+1)+sigma(2*i-1)+sigma(i/2^k)*2^(k+1)-6*i-2;

k:=0; j:=n-i; while j mod 2<>1 do k:=k+1; j:=j/2; od;

b:=sigma(2*(n-i)+1)+sigma(2*(n-i)-1)+sigma((n-i)/2^k)*2^(k+1)-6*(n-i)-2;

if a=b and a=n then print(n); fi; od; od; end: P(10^6);

CROSSREFS

Cf. A066272, A066417, A210732.

Sequence in context: A160853 A235099 A332421 * A282557 A200709 A248657

Adjacent sequences:  A227974 A227975 A227976 * A227978 A227979 A227980

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Oct 07 2013

EXTENSIONS

a(5)-a(7) from Giovanni Resta, Oct 08 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 24 20:35 EDT 2021. Contains 348233 sequences. (Running on oeis4.)