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A238905 The tau(sigma)-perfect numbers, where the set of f-perfect numbers for an arithmetical function f is defined in A066218.

%I A238905 #15 Aug 22 2023 11:58:57
%S A238905 6,15,22,33,39,57,69,111,129,141,183,201,214,219,237,309,453,471,489,
%T A238905 573,579,633,669,813,831,849,939,993,1101,1149,1191,1263,1371,1389,
%U A238905 1461,1519,1569,1623,1641,1821,1839,1893,1942,1983,2019,2073,2199,2253,2271
%N A238905 The tau(sigma)-perfect numbers, where the set of f-perfect numbers for an arithmetical function f is defined in A066218.
%H A238905 Amiram Eldar, <a href="/A238905/b238905.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Paolo P. Lava)
%e A238905 Aliquot divisors of 39 are 1, 3, 13. Then tau(sigma(1)) + tau(sigma(3)) + tau(sigma(13)) = 1 + 3 + 4 = 8 and tau(sigma(39)) = 8.
%p A238905 with(numtheory); P:=proc(q) local a,b,i,n;
%p A238905 for n from 1 to q do a:=divisors(n); b:=0;
%p A238905 for i from 1 to nops(a)-1 do b:=b+tau(sigma(a[i])); od;
%p A238905 if tau(sigma(n))=b then print(n); fi; od; end: P(10^6);
%t A238905 q[n_] := DivisorSum[n, DivisorSigma[0, DivisorSigma[1, #]] &, # < n &] == DivisorSigma[0, DivisorSigma[1, n]]; Select[Range[2300], q] (* _Amiram Eldar_, Aug 22 2023 *)
%o A238905 (PARI) isok(n) = numdiv(sigma(n)) == sumdiv(n, d, (d<n)*numdiv(sigma(d))); \\ _Michel Marcus_, Mar 08 2014
%Y A238905 Cf. A000005, A000230, A066218.
%K A238905 nonn,easy
%O A238905 1,1
%A A238905 _Paolo P. Lava_, Mar 07 2014