A333930 Larger of recursive amicable numbers pair: numbers m < k such that m = s(k) and k = s(m), where s(k) = A333926(k) - k is the sum of proper recursive divisors of k.

284, 378, 2924, 4584, 5564, 16632, 16728, 28752, 30912, 53692, 76084, 69552, 87633, 124155, 139815, 179118, 168730, 225096, 202444, 256338, 245904, 266568, 365084, 389924, 320016, 430402, 391656, 353616, 387720, 393528, 486178, 525915, 555216, 642720, 814698, 682896

Offset

1,1

Comments

The terms are ordered according to their lesser counterparts (A333929).

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

284 is a terms since A333926(284) - 284 = 220 and A333926(220) - 220 = 284.

Mathematica

recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; recDivSum[1] = 1; recDivSum[n_] := Times @@ (f @@@ FactorInteger[n]); s[n_] := recDivSum[n] - n; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 1, 10^5}]; seq

Crossrefs

Cf. A333926, A333927, A333929.

Analogous sequences: A002046, A002953 (unitary), A126166 (exponential), A126170 (infinitary), A292981 (bi-unitary).

Sequence in context: A285890 A356219 A061310 * A259996 A092681 A090789

Adjacent sequences: A333927 A333928 A333929 * A333931 A333932 A333933

Keyword

nonn

Author

Amiram Eldar, Apr 10 2020

Status

approved