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

1288, 2773, 1485, 2773, 5775, 11903, 6128, 11903, 8008, 19693, 11685, 19693, 16744, 36049, 19305, 36049, 21896, 47141, 25245, 47141, 24472, 52687, 28215, 52687, 26488, 61993, 35505, 61993, 32620, 78061, 45441, 78061, 37352, 80417, 43065, 80417, 39928, 85963

Offset: 1

Author

Michel Lagneau, Mar 31 2014

Keywords

• nonn

Comments

Property of the sequence:

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.

Examples

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

Links

• Michel Lagneau, Table of n, a(n) for n = 1..38

Crossrefs

Cf. A000203, A239436.

Programs

Mathematica

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-François Alcover, adapted for this sequence. See A239436 *)