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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 January 18 09:26 EST 2022. Contains 350454 sequences. (Running on oeis4.)