A292980 Smaller of bi-unitary amicable pair.

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

Author

Amiram Eldar, Sep 27 2017

Keywords

• nonn

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.

Examples

			3608 is in the sequence since A188999(3608) - 3608 = 3952 and A188999(3952) - 3952 = 3608.
		

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.
• David Moews, Perfect, amicable and sociable numbers.

Crossrefs

Cf. A002025, A188999, A292981.

Programs

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 *)