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A239939 Members of a pair (m,n) such that sigma(m) = sigma(n) = sigma(n-m), m < n where sigma = A000203. 1

%I #30 Nov 30 2014 14:46:34

%S 1288,2773,1485,2773,5775,11903,6128,11903,8008,19693,11685,19693,

%T 16744,36049,19305,36049,21896,47141,25245,47141,24472,52687,28215,

%U 52687,26488,61993,35505,61993,32620,78061,45441,78061,37352,80417,43065,80417,39928,85963

%N Members of a pair (m,n) such that sigma(m) = sigma(n) = sigma(n-m), m < n where sigma = A000203.

%C Property of the sequence:

%C The sequence is of the form a1, a1+a2, a2, a1+a2, a3, a3+a4, a4, a3+a4, a5, a5+a6, a6,... where {a1, a2, a3,...} = A239436 are the members of a pair (m,n) such that sigma(m) = sigma(n) = sigma(n+m), and where the members a1+a2, a3+a4, a5+a6,... are repeated two times.

%H Michel Lagneau, <a href="/A239939/b239939.txt">Table of n, a(n) for n = 1..38</a>

%e The pair (1288, 2773) is in the sequence because sigma(1288) = sigma(2773) = 2880 and sigma(2773-1288) = sigma(1485) = 2880.

%t a[n1_, n2_] := (t = Table[{DivisorSigma[1, n], n}, {n, n1, n2}] // Sort; s = Select[Split[t, #1[[1]] == #2[[1]] &], Length[#] >= 2 &]; f[lst_] := Select[Table[{lst[[i]], lst[[j]]}, {i, 1, Length[lst] - 1}, {j, i + 1, Length[lst]}] // Flatten[#, 1] &, #[[1, 1]] == DivisorSigma[1, #[[1, 2]] - #[[2, 2]]] &]; Select[f /@ s, # != {} &]); Flatten[a[1, 10^5], 2][[All, 2]] (* Program from Jean-Fran├žois Alcover, adapted for this sequence. See A239436 *)

%Y Cf. A000203, A239436.

%K nonn

%O 1,1

%A _Michel Lagneau_, Mar 31 2014

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Last modified April 21 07:21 EDT 2024. Contains 371850 sequences. (Running on oeis4.)