A126160 -id:A126160 - cp's OEIS frontend

48, 75, 140, 195, 1050, 1925, 1575, 1648, 2024, 2295, 5775, 6128, 8892, 16587, 9504, 20735, 62744, 75495, 186615, 206504, 196664, 219975, 199760, 309135, 266000, 507759, 312620, 549219, 526575, 544784, 573560, 817479, 587460, 1057595, 1000824, 1902215, 1081184, 1331967, 1139144, 1159095, 1140020, 1763019

Offset: 1

Omar E. Pol, Oct 14 2019

nonn

Also called betrothed pairs, or quasiamicable pairs, or reduced amicable pairs.
A pair of numbers x and y is called quasi-amicable if sigma(x) = sigma(y) = x + y + 1, where sigma(n) is the sum of the divisors of n.
All known quasi-amicable pairs have opposite parity.
First differs from A005276 at a(6).
According to Hisanori Mishima (see link) there are 404 quasi-amicable pairs where the smaller part is less than 10^10. See A126160 for more values. - Peter Luschny, Nov 18 2019

			Initial quasi-amicable pairs:
    48,   75;
   140,  195;
  1050, 1925;
  1575, 1648;
  2024, 2295;
...
The sum of the divisors of 48 is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 124. On the other hand the sum of the divisors of 75 is 1 + 3 + 5 + 15 + 25 + 75 = 124. Note that 48 + 75 + 1 = sigma(48) = sigma(75) = 124. The smallest quasi-amicable pair is (48, 75), so a(1) = 48 and a(2) = 75.

R. K. Guy, Unsolved Problems in Number Theory, B5.
P. Hagis and G. Lord, Quasi-amicable numbers, Math. Comp. 31 (1977), 608-611.
Hisanori Mishima, Table of quasi-amicable pairs under 10^10.
Paul Pollack, Quasi-Amicable Numbers are Rare, Journal of Integer Sequences, Vol. 14 (2011), Article 11.5.2.
Eric Weisstein's World of Mathematics, Quasiamicable Pair.

A003502 and A003503 interleaved.

Cf. A000203, A005276, A126160, A179612, A259180.

with(numtheory): aList := proc(searchbound)
local r, n, m, L: L := []:
for m from 1 to searchbound do
   n := sigma(m) - m - 1:
   if n <= m then next fi;
   r := sigma(n) - n - 1:
   if r = m then L := [op(L), m, n] fi;
od; L end:
aList(10000); # Peter Luschny, Nov 18 2019

a(2*n-1) = A003502(n); a(2*n) = A003503(n).

cp's OEIS Frontend

A328370 Quasi-amicable pairs.

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