A333929 Lesser 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.

220, 366, 2620, 3864, 5020, 16104, 16536, 26448, 29760, 43524, 63020, 67344, 69615, 100485, 122265, 142290, 142310, 196248, 196724, 198990, 239856, 240312, 280540, 308620, 309264, 319550, 326424, 341904, 348840, 366792, 469028, 522405, 537744, 580320, 647190, 661776

Offset

1,1

Comments

The larger counterparts are in A333930.

Links

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

Example

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

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, n]], {n, 1, 10^5}]; seq

Crossrefs

Cf. A333926, A333927, A333930.

Analogous sequences: A002025, A002952 (unitary), A126165 (exponential), A126169 (infinitary), A292980 (bi-unitary).

Sequence in context: A328063 A328065 A287011 * A157107 A175738 A260203

Adjacent sequences: A333926 A333927 A333928 * A333930 A333931 A333932

Keyword

nonn

Author

Amiram Eldar, Apr 10 2020

Status

approved