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.

154, 3136, 5536, 20066, 136036, 9550080, 78011830

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 A368138

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