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Amicable pairs where only deficient aliquot parts are considered.
1

%I #12 Jan 27 2019 05:10:54

%S 1184,1210,6232,6368,10744,10856,66928,66992,522405,525915,643336,

%T 652664,5459176,5495264,7677248,7684672,16137628,16150628,25596544,

%U 25640096,26090325,26138475,28118032,28128368,34364912,34380688,133178325,133471275,164733752,166212808

%N Amicable pairs where only deficient aliquot parts are considered.

%C Subsequence of A063990.

%e Deficient aliquot parts of 1184 are 1,2,4,8,16,32,37,74,148,296,592 and their sum is 1210.

%e Deficient aliquot parts of 1210 are 1,2,5,10,11,22,55,110,121,242,605 and their sum is 1184.

%p with(numtheory): P:=proc(q) local a,b,c,d,k,n; for n from 1 to q do

%p a:=sort([op(divisors(n))]); b:=0; for k from 1 to nops(a)-1 do if 2*a[k]>sigma(a[k]) then b:=b+a[k]; fi; od;

%p c:=sort([op(divisors(b))]); d:=0; for k from 1 to nops(c)-1 do if 2*c[k]>igma(c[k]) then d:=d+c[k]; fi; od; if d=n and d<>b then print(n); fi; od; end: P(10^6);

%t defQ[n_] := DivisorSigma[1,n] < 2n; s[n_] := DivisorSum[n, #&, #<n && defQ[#]&]; seq={}; Do[m=s[n]; If[m>n && s[m]==n, AppendTo[seq, {n,m}]], {n, 1, 10^5}]; Flatten[seq] (* _Amiram Eldar_, Jan 26 2019 *)

%Y Cf. A063990, A259180, A280515.

%K nonn,tabf

%O 1,1

%A _Paolo P. Lava_, Jan 04 2017

%E More terms from _Amiram Eldar_, Jan 26 2019