A371422 - OEIS

%I #8 Mar 23 2024 08:23:04

%S 12,14,15,23,29,42,44,48,54,56,60,62,65,66,69,70,72,75,76,77,78,83,84,

%T 85,86,87,88,90,91,92,94,95,99,102,107,108,110,111,112,114,115,117,

%U 118,119,120,123,124,125,128,129,131,132,134,135,136,137,139,140,142

%N Numbers whose aliquot-like sequence based on the largest aliquot divisor of the sum of divisors of n (A371418) terminates in a cycle of length 2.

%C It is unknown whether 222 is a term of this sequence or not (see A371423).

%H Amiram Eldar, <a href="/A371422/b371422.txt">Table of n, a(n) for n = 1..108</a>

%H 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 12 is a term because when we start with 12 and repeatedly apply the mapping x -> A371418(x), we get the sequence 12, 14, 12, 14, ...

%e 76 is a term because when we start with 76 and repeatedly apply the mapping x -> A371418(x), we get the sequence 76, 70, 72, 65, 42, 48, 62, 48, 62, ...

%t r[n_] := n/FactorInteger[n][[1, 1]]; f[n_] := r[DivisorSigma[1, n]];

%t q[n_] := Module[{m = NestWhileList[f, n, UnsameQ, All][[-1]], k}, k = f[m]; k != m && f[k] == m]; Select[Range[221], q]

%Y Cf. A371418, A371421, A371423.

%Y Similar sequences: A127655, A127660, A127665.

%K nonn

%O 1,1

%A _Amiram Eldar_, Mar 23 2024