A239436 Members of a pair (m,k) such that sigma(m) = sigma(k) = sigma(m+k), m < k where sigma = A000203.

1288, 1485, 5775, 6128, 8008, 11685, 16744, 19305, 21896, 25245, 24472, 28215, 26488, 35505, 32620, 45441, 37352, 43065, 39928, 46035, 47656, 54945, 50260, 65637, 52808, 60885, 55384, 63855, 62744, 75495, 72772, 79365, 68264, 78705, 75075, 79664, 80584, 90915

Offset: 1

Author

Michel Lagneau, Mar 18 2014

Keywords

• nonn

Comments

The numbers such that sigma(k) = sigma(m) = m+k+1 and m+k is prime are in the sequence since sigma(k+m) = m+k+1 (see A005276). - Giovanni Resta, Mar 20 2014

Examples

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A005276.

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]] (* Jean-François Alcover, Mar 20 2014 *)

Extensions

More terms from Jean-François Alcover, Mar 20 2014