A322162 Numbers k such that bsigma(k) = 2k + 2, where bsigma(k) is the sum of bi-unitary divisors of k (A188999).

80, 104, 832, 1952, 7424, 62464, 522752, 8382464, 33357824, 134193152, 267649024, 17167286272, 549754241024

Offset: 1

Author

Amiram Eldar, Nov 29 2018

Keywords

• nonn
• more

Comments

The bi-unitary version of A088831.

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.

Examples

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

Crossrefs

Cf. A050414, A088831, A188999.

Programs

Mathematica

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 &]

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)));
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

Extensions

a(13) from Giovanni Resta, Dec 01 2018