OFFSET
1,1
COMMENTS
The terms are arranged by the order of their lesser counterparts (A109797). - Amiram Eldar, Oct 26 2019
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
J. M. Sachs, Admirable Numbers and Compatible Pairs, The Arithmetic Teacher, Vol. 7, No. 6 (1960), pp. 293-295.
T. Trotter, Admirable Numbers. [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - N. J. A. Sloane, Mar 29 2018]
EXAMPLE
sigma(42)-2(1)=96-2=94 and sigma(52)-2(2)=98-4=94 and 42+52=94 so a(4)=52.
MAPLE
L:=remove(proc(z) isprime(z) end, [$1..10000]): S:=proc(n) map(proc(z) sigma(n) -2*z end, divisors(n) minus {n}) end; CK:=map(proc(z) [z, S(z)] end, L): CL:=[]: for j from 1 to nops(CK)-1 do x:=CK[j, 1]; sx:=sigma(x); Sx:=CK[j, 2]; for k from j+1 to nops(CK) while CK[k, 1]<sx do y:=CK[k, 1]; if x+y in Sx intersect CK[k, 2] then CL:=[op(CL), [x, y, x+y]] fi od od;
MATHEMATICA
seq = {}; Do[d = Most[Divisors[n]]; s = Total[d]; Do[m = s - 2*d[[k]]; If[m <= 0 || m <= n, Continue[]]; delta = DivisorSigma[1, m] - m - n; If[delta > 0 && EvenQ[delta] && delta/2 < m && Divisible[m, delta/2], AppendTo[seq, m]], {k, Length[d], 1, -1}], {n, 1, 750}]; seq (* Amiram Eldar, Oct 26 2019 *)
KEYWORD
nonn
AUTHOR
Walter Kehowski, Aug 15 2005
STATUS
approved