A333930 - OEIS

%I #9 Apr 12 2020 09:50:55

%S 284,378,2924,4584,5564,16632,16728,28752,30912,53692,76084,69552,

%T 87633,124155,139815,179118,168730,225096,202444,256338,245904,266568,

%U 365084,389924,320016,430402,391656,353616,387720,393528,486178,525915,555216,642720,814698,682896

%N 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.

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

%H Amiram Eldar, <a href="/A333930/b333930.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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

%Y Cf. A333926, A333927, A333929.

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

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 10 2020