A322162 - OEIS

%I #15 Jul 17 2021 06:57:56

%S 80,104,832,1952,7424,62464,522752,8382464,33357824,134193152,

%T 267649024,17167286272,549754241024

%N Numbers k such that bsigma(k) = 2k + 2, where bsigma(k) is the sum of bi-unitary divisors of k (A188999).

%C The bi-unitary version of A088831.

%C If m is a term of A050414, i.e., 2^m - 3 is prime, then 2^(2*m-2) * (2^m-3) is in this sequence, and also 2^(m-1) * (2^m-3) if m is even.

%e 80 is in this sequence since its sum of bi-unitary divisors is 162 = 2 * 80 + 2.

%t fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; Select[Range[2,10000], Times@@(fun @@@ FactorInteger[#]) == 2#+2 &]

%o (PARI) bsigma(n,f=factor(n))=prod(i=1,#f~, my(p=f[i,1], e=f[i, 2]); if (e%2, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1) -p^(e/2)));

%o forfactored(n=1,10^8, if(bsigma(n[1],n[2])==2*n[1]+2, print1(n[1]", "))) \\ _Charles R Greathouse IV_, Nov 29 2018

%Y Cf. A050414, A088831, A188999.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Nov 29 2018

%E a(13) from _Giovanni Resta_, Dec 01 2018