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 A322162 Numbers k such that bsigma(k) = 2k + 2, where bsigma(k) is the sum of bi-unitary divisors of k (A188999). 0
 80, 104, 832, 1952, 7424, 62464, 522752, 8382464, 33357824, 134193152, 267649024, 17167286272, 549754241024 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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. LINKS Table of n, a(n) for n=1..13. EXAMPLE 80 is in this sequence since its sum of bi-unitary divisors is 162 = 2 * 80 + 2. 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 &] PROG (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 CROSSREFS Cf. A050414, A088831, A188999. Sequence in context: A119482 A054983 A039545 * A143755 A105449 A223084 Adjacent sequences: A322159 A322160 A322161 * A322163 A322164 A322165 KEYWORD nonn,more AUTHOR Amiram Eldar, Nov 29 2018 EXTENSIONS a(13) from Giovanni Resta, Dec 01 2018 STATUS approved

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Last modified February 23 15:29 EST 2024. Contains 370283 sequences. (Running on oeis4.)