

A322162


Numbers k such that bsigma(k) = 2k + 2, where bsigma(k) is the sum of biunitary divisors of k (A188999).


0



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

1,1


COMMENTS

The biunitary version of A088831.
If m is a term of A050414, i.e., 2^m  3 is prime, then 2^(2*m2) * (2^m3) is in this sequence, and also 2^(m1) * (2^m3) if m is even.


LINKS

Table of n, a(n) for n=1..13.


EXAMPLE

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


MATHEMATICA

fun[p_, e_] := If[OddQ[e], (p^(e+1)1)/(p1), (p^(e+1)1)/(p1)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)/(p1), (p^(e+1)1)/(p1) 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



