login
a(n) = A023194 - A062700(n). Negative values of A071166(m) = m-A006530(A000203(m)) differences. In these cases m is square number from A023194.
1

%I #13 Jul 03 2024 22:13:13

%S -1,-3,-4,-15,-6,-63,-18,-364,-42,-400,-60,-4095,-72,-90,-102,-3906,

%T -132,-168,-2380,-174,-65535,-5220,-294,-384,-262143,-12720,-678,-702,

%U -265720,-744,-762,-774,-828,-840,-25260,-858,-912,-1092,-1098,-1164,-1182,-1194,-1218,-1374,-1428,-1488,-1560

%N a(n) = A023194 - A062700(n). Negative values of A071166(m) = m-A006530(A000203(m)) differences. In these cases m is square number from A023194.

%F Values of m - A006530(A000203(m)) differences, when m < A006530(A000203(m)).

%e m=29929=173, sigma[29929]=1+173+29929=30103 and 29929-30103=-174, the 20th term here.

%t ma[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] Do[s=n-ma[DivisorSigma[1, n]]; If[Equal[Sign[s], -1], Print[s]], {n, 2, 10000000}]

%o (PARI) for(n=1,1e3,if(isprime(s=sigma(n^2)),print1(n^2-s", "))) \\ _Charles R Greathouse IV_, Feb 19 2013

%Y Cf. A000203, A006530, A062700, A023194, A071166.

%K sign

%O 1,2

%A _Labos Elemer_, May 15 2002