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A292980
Smaller of bi-unitary amicable pair.
11
114, 594, 1140, 3608, 4698, 5940, 6232, 7704, 9520, 10744, 12285, 13500, 41360, 44772, 46980, 60858, 62100, 67095, 67158, 73360, 79650, 79750, 105976, 118500, 141664, 142310, 177750, 185368, 193392, 217840, 241024, 298188, 308220, 308992, 356408, 399200
OFFSET
1,1
COMMENTS
Analogous to amicable numbers with bi-unitary sigma (A188999) instead of sigma (A000203).
Hagis found all the bi-unitary amicable pairs with smaller members below 10^6.
The larger members are in A292981.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..6368 (all terms below 2*10^11, from David Moews' site).
Peter Hagis, Jr., Bi-unitary amicable and multiperfect numbers, Fibonacci Quarterly, Vol. 25, No. 2 (1987), pp. 144-150.
EXAMPLE
3608 is in the sequence since A188999(3608) - 3608 = 3952 and A188999(3952) - 3952 = 3608.
MATHEMATICA
fun[p_, e_]:=If[Mod[e, 2]==1, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)];
bsigma[n_] := If[n==1, 1, Times @@ (fun @@@ FactorInteger[n])]; Do[s = bsigma[n]; If[s > 2 n && bsigma[s - n] == s, Print[n]], {n, 1, 10000}] (* Amiram Eldar, Sep 29 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 27 2017
STATUS
approved