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A371421 Numbers whose aliquot-like sequence based on the largest aliquot divisor of the sum of divisors of n (A371418) terminates in a fixed point.

%I A371421 #10 Jun 21 2025 07:54:08
%S A371421 1,2,3,4,5,6,7,8,9,10,11,13,16,17,18,19,20,21,22,24,25,26,27,28,30,31,
%T A371421 32,33,34,35,36,37,38,39,40,41,43,45,46,47,49,50,51,52,53,55,57,58,59,
%U A371421 61,63,64,67,68,71,73,74,79,80,81,82,89,93,96,97,98,100,101
%N A371421 Numbers whose aliquot-like sequence based on the largest aliquot divisor of the sum of divisors of n (A371418) terminates in a fixed point.
%C A371421 It is unknown whether 222 is a term of this sequence or not (see A371423).
%H A371421 Amiram Eldar, <a href="/A371421/b371421.txt">Table of n, a(n) for n = 1..113</a>
%H A371421 Robert D. Carmichael, <a href="https://doi.org/10.5951/MT.14.6.0305">Empirical Results in the Theory of Numbers</a>, The Mathematics Teacher, Vol. 14, No. 6 (1921), pp. 305-310; <a href="https://www.jstor.org/stable/27950349">alternative link</a>. See p. 309.
%e A371421 3 is a term because when we start with 3 and repeatedly apply the mapping x -> A371418(x), we get the sequence 3, 2, 1, 1, 1, ...
%e A371421 40 is a term because when we start with 40 and repeatedly apply the mapping x -> A371418(x), we get the sequence 40, 45, 39, 28, 28, 28, ...
%t A371421 r[n_] := n/FactorInteger[n][[1, 1]]; f[n_] := r[DivisorSigma[1, n]]; q[n_] := Module[{m = NestWhileList[f, n, UnsameQ, All][[-1]]}, f[m] == m]; Select[Range[221], q]
%Y A371421 Cf. A371418, A371422, A371423.
%Y A371421 A023194 is a subsequence.
%Y A371421 Cf. A063769, A080907.
%K A371421 nonn
%O A371421 1,2
%A A371421 _Amiram Eldar_, Mar 23 2024