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

1,1

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.

David Moews, Perfect, amicable and sociable numbers.

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

Cf. A002025, A188999, A292981.

Sequence in context: A122279 A251481 A251475 * A126169 A324708 A353746

Adjacent sequences: A292977 A292978 A292979 * A292981 A292982 A292983

Keyword

nonn

Author

Amiram Eldar, Sep 27 2017

Status

approved