A109798 Second of a pair of compatible numbers, where two numbers m and n are compatible if sigma(n)-2dn=sigma(m)-2dm=m+n, for some proper divisors dn and dm of m and n respectively.

28, 40, 42, 52, 60, 96, 102, 104, 124, 110, 182, 182, 188, 210, 230, 234, 184, 358, 362, 204, 312, 248, 252, 408, 372, 424, 306, 388, 418, 434, 376, 516, 384, 508, 530, 638, 782, 572, 888, 782, 828, 872, 592, 644, 820, 650, 938, 908, 1026, 1034, 1102, 976, 760

Offset: 1

Author

Walter Kehowski, Aug 15 2005

Keywords

• nonn

Comments

The terms are arranged by the order of their lesser counterparts (A109797). - Amiram Eldar, Oct 26 2019

Examples

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

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.

Crossrefs

Cf. A109797, A111592.

Programs

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]
				

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 *)