A239436 - OEIS

%I #27 Feb 17 2024 23:43:37

%S 1288,1485,5775,6128,8008,11685,16744,19305,21896,25245,24472,28215,

%T 26488,35505,32620,45441,37352,43065,39928,46035,47656,54945,50260,

%U 65637,52808,60885,55384,63855,62744,75495,72772,79365,68264,78705,75075,79664,80584,90915

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

%C 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

%H Giovanni Resta, <a href="/A239436/b239436.txt">Table of n, a(n) for n = 1..10000</a>

%e The pair (1288, 1485) is in the sequence because sigma(1288) = sigma(1485) = 2880 and sigma(1288+1485) = sigma(2773) = 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]] (* _Jean-François Alcover_, Mar 20 2014 *)

%Y Cf. A000203, A005276.

%K nonn

%O 1,1

%A _Michel Lagneau_, Mar 18 2014

%E More terms from _Jean-François Alcover_, Mar 20 2014