1,1

Compatible numbers were introduced by Sachs in analogy to amicable numbers, as admirable numbers are analogous to perfect numbers. Some terms have more than one counterpart (A109798), like 80 (two counterparts: 102 and 104) or 156 (3 counterparts: 210, 230 and 234). - Amiram Eldar, Oct 26 2019

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.

sigma(42)-2(1)=96-2=94 and sigma(52)-2(2)=98-4=94 and 42+52=94 so a(4)=42.

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;

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, n]], {k, Length[d], 1, -1}], {n, 1, 750}]; seq (* Amiram Eldar, Oct 26 2019 *)

Cf. A109798, A111592.

Sequence in context: A284174 A292982 A334972 * A129656 A372299 A334974

Adjacent sequences: A109794 A109795 A109796 * A109798 A109799 A109800

Walter Kehowski, Aug 15 2005

approved