cp's OEIS Frontend

A273992 Numbers whose sum of anti-divisors is equal to the sum of its unitary divisors.

%I A273992 #13 Jul 12 2022 08:30:27
%S A273992 11,22,33,65,82,140,218,228,483,537,616,1184,2889,6430,10216,15849,
%T A273992 21541,59620,112590,117818,130356,483153,3028671,3589646,7231219,
%U A273992 8515767,13050345,36494625,44498344,50414595,217728002,459644211,519061576,1217532421,1573368218
%N A273992 Numbers whose sum of anti-divisors is equal to the sum of its unitary divisors.
%e A273992 Sum of anti-divisors of 11 is 12. Unitary divisors of 11 are 1, 11 and their sum is 12.
%p A273992 with(numtheory): P:=proc(q) local a,b,c,j,k,n;
%p A273992 for n from 1 to q do k:=0; j:=n;
%p A273992 while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
%p A273992 a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
%p A273992 c:=ifactors(n)[2]; b:=mul(c[j][1]^c[j][2]+1,j=1..nops(c));
%p A273992 if a=b then print(n); fi; od; end: P(10^6);
%t A273992 Select[Range[5000], Function[n, Total[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]] == Plus @@ Select[Divisors@ n, GCD[#, n/#] == 1 &]]] (* _Michael De Vlieger_, Jun 06 2016, after _Robert G. Wilson v_ at A034448 and _Harvey P. Dale_ at A066272 *)
%o A273992 (PARI) sud(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));
%o A273992 sad(n) = my(k); if(n>1, k=valuation(n, 2); sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2, 0);
%o A273992 isok(n) = sad(n) == sud(n); \\ _Michel Marcus_, Jun 12 2016
%Y A273992 Cf. A034448, A066417, A074751, A178029.
%K A273992 nonn
%O A273992 1,1
%A A273992 _Paolo P. Lava_, Jun 06 2016
%E A273992 a(23)-a(26) from _Michel Marcus_, Jun 12 2016
%E A273992 a(27)-a(35) from _Amiram Eldar_, Jul 12 2022