Search: id:A109797
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%I A109797
%S A109797 24,30,40,42,48,60,80,80,96,102,126,140,140,156,156,156,174,180,180,198,
%T A109797 216,224,224,264,276,280,294,294,300,320,340,372,380,384,440,440,468,
%U A109797 500,504,510,528,560,582,608,616,642,680,684,690,690,696,702,736,750
%N A109797 First 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.
%H A109797 T. Trotter, <a href="http://www.trottermath.net/numthry/admirabl.html">
               Admirable Numbers.</a>
%e A109797 sigma(42)-2(1)=96-2=94 and sigma(52)-2(2)=98-4=94 and 42+52=94 so a(4)=42.
%p A109797 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;
%Y A109797 Cf. A111592.
%Y A109797 Sequence in context: A075422 A098030 A068544 this_sequence A129656 A048945 
               A111398
%Y A109797 Adjacent sequences: A109794 A109795 A109796 this_sequence A109798 A109799 
               A109800
%K A109797 nonn
%O A109797 1,1
%A A109797 Walter A. Kehowski (wkehowski(AT)cox.net), Aug 15 2005

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