A292981 Larger of bi-unitary amicable pair.

126, 846, 1260, 3952, 5382, 8460, 6368, 8496, 13808, 10856, 14595, 17700, 51952, 49308, 53820, 83142, 62700, 71145, 73962, 97712, 107550, 88730, 108224, 131100, 153176, 168730, 196650, 203432, 195408, 287600, 309776, 306612, 365700, 332528, 399592, 419800

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 smaller members are in A292980.

The terms are ordered according to their lesser counterparts.

Links

Amiram Eldar, Table of n, a(n) for n = 1..6368 (all terms with lesser member 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

3952 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[s-n]], {n, 1, 10000}] (* Amiram Eldar, Sep 29 2018 *)

Crossrefs

Cf. A002046, A188999, A292980.

Sequence in context: A107658 A181254 A004008 * A126170 A324709 A342307

Adjacent sequences: A292978 A292979 A292980 * A292982 A292983 A292984

Keyword

nonn

Author

Amiram Eldar, Sep 27 2017

Status

approved